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ABSTRACT

ABSTRACT:

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Steganography is the art and science of hiding secret data in plain sight

without being noticed within an innocent cover data so that it can be

securely transmitted over a network. The word Steganography is originally

composed of two Greek words steganos and graphia, which means

"covered writing". The use of Steganography dates back to ancient times

where it was used by romans and ancient Egyptians. The interest in

modem digital Steganography started by Simmons in 1983 when he

presented the problem of two prisoners wishing to escape and being

watched by the warden that blocks any suspicious data communicated

between them and passes only normal looking one. Any digital file such as

image, video, audio, text or IP packets can be used to hide secret

message. Generally the file used to hide data is referred to as cover

object, and the term stego-object is used for the file containing secret

message. Among all digital file formats available nowadays image files are

the most popular cover objects because they are easy to find and have

higher degree of distortion tolerance over other types of files with high

hiding capacity due to the redundancy of digital information

representation of an image data. There are a number of steganographic

schemes that hide secret message in an image file; these schemes can be

classified according to the format of the cover image or the method of

hiding. We have two popular types of hiding methods; spatial domain

embedding and transform domain embedding.

Steganography gained importance in the past few years due to the

increasing need for providing secrecy in an open environment like the

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internet. With almost anyone can observe the communicated data all

around, Steganography attempts to hide the very existence of the

message and make communication undetectable. Many techniques are

used to secure information such as cryptography that aims to scramble

the information sent and make it unreadable while Steganography is used

to conceal the information so that no one can sense its existence. In most

algorithms used to secure information both Steganography and

cryptography are used together to secure a part of information.

Steganography has many technical challenges such as high hiding

capacity and imperceptibility. In this paper, we try to optimize these two

main requirements by proposing a novel technique for hiding data in

digital images by combining the use of adaptive hiding capacity function

that hides secret data in the integer wavelet coefficients of the cover

image with the optimum pixel adjustment (OPA) algorithm. The

coefficients used are selected according to a pseudorandom function

generator to increase the security of the hidden data. The OPA algorithm

is applied after embedding secret message to minimize the embedding

error. The proposed system showed high hiding rates with reasonable

imperceptibility compared to other steganographic systems.

Existing Methods:

LSB Embedding in Spatial Domain

The basic idea in LSB is the direct replacement of LSBs of noisy

or unused bits of the cover image with the secret message bits.

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Till now LSB is the most preferred technique used for data hiding

because it is simple to implement offers high hiding capacity, and

provides a very easy way to control stego-image quality

Drawbacks of Existing Method:

Low hiding capacity and Complex computations

Embedding error will be there(Overflow & Underflow)

Proposed Method:

The proposed system is an adaptive data hiding scheme, in which

randomly selected integer wavelet coefficients of the cover image

are modified with secret message bits.

Each of these selected coefficients hide different number of

message bits according to the hiding capacity function.

After data insertion we apply optimum pixel adjustment algorithm

to reduce the error induced due to data insertion.

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TABLE OF CONTENTS

TABLE OF CONTENTS

CHAPTER NO. PAGE NO.

Abstract 2

CHAPTER 1

1.1 Introduction 7

1.2 Block diagram 10

1.3 Fundamental of digital image 11

CHAPTER 2

2.1 Introduction about Wavelet 24

2.2 Wavelet Transform 27

2.3 Lifting Scheme 47

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2.4 Lifting using Haar 48

CHAPTER 3

3.1 Introduction to LSB 51

3.2 Data hiding by simple LSB substitution 54

3.3 Optimal pixel adjustment process 56

CHAPTER 4

4.1 Introduction to Matlab 59

4.2 Starting to Matlab 60

CHAPTER 5

5.1 Conclusion 83

5.2 Reference 83

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CHAPTER 1

1.1 Introduction:

Steganography is the art and science of hiding secret data in plain sight

without being noticed within an innocent cover data so that it can be securely

transmitted over a network. The word Steganography is originally composed of

two Greek wordssteganos andgraphic, which means "covered writing". The

use of Steganography dates back to ancient times where it was used by romans

and ancient Egyptians.

The interest in modem digital Steganography started by Simmons in 1983

when he presented the problem of two prisoners wishing to escape and being

watched by the warden that blocks any suspicious data communicated between

them and passes only normal looking one. Any digital file such as image, video,

audio, text or IP packets can be used to hide secret message.

Generally the file used to hide data is referred to as cover object, and the

term stego-object is used for the file containing secret message.

Among all digital file formats available nowadays image files are the

most popular cover objects because they are easy to find and have higher degree

of distortion tolerance over other types of files with high hiding capacity due to

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the redundancy of digital information representation of an image data. There are

a number of steganographic schemes that hide secret message in an image file;

these schemes can be classified according to the format of the cover image or

the method of hiding. We have two popular types of hiding methods; spatial

domain embedding and transform domain embedding.

The Least Significant Bit (LSB) substitution is an example of spatial

domain techniques. The basic idea in LSB is the direct replacement of LSBs of

noisy or unused bits of the cover image with the secret message bits. Till now

LSB is the most preferred technique used for data hiding because it is simple to

implement offers high hiding capacity, and provides a very easy way to control

stego-image quality but it has low robustness to modifications made to the

stego-image such as low pass filtering and compression and also low

imperceptibility. Algorithms using LSB in grayscale images can be found in.

The other type of hiding method is the transform domain techniques

which appeared to overcome the robustness and imperceptibility problems

found in the LSB substitution techniques. There are many transforms that can

be used in data hiding, the most widely used transforms are; the discrete

cosine transform (DCT) which is used in the common image compression

format JPEG and MPEG, the discrete wavelet transform (DWT) and the discreteFourier transform (DFT).

Examples to data hiding using DCT can be found in. Most recent

researches are directed to the use of DWT since it is used in the new image

compression format JPEG2000 and MPEG4, examples of using DWT can be

found in. In the secret message is embedded into the high frequency coefficients

of the wavelet transform while leaving the low frequency coefficients sub band

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unaltered. While in an adaptive (varying) hiding capacity function is employed

to determine how many bits of the secret message is to be embedded in each of

the wavelet coefficients. The advantages of transform domain techniques over

spatial domain techniques are their high ability to tolerate noises and some

Signal processing operations but on the other hand they are computationally

complex and hence slower. In all proposed techniques for Steganography

whether spatial or transform the key problem is how to increase the size of the

Secret message without causing noticeable distortions in the cover object. Some

of these techniques try to achieve the high hiding capacity low distortion result

by using adaptive techniques that calculate the hiding capacity of the cover

According to its local characteristics as in.

However, the steganographic transform-based techniques have the

following disadvantages; low hiding capacity and complex computations. Thus,

to get over these disadvantages, the present paper proposes an adaptive data

Hiding technique joined with the use of optimum pixel adjustment algorithm tohide data into the integer wavelet coefficients of the cover image in order to

maximize the hiding capacity as much as possible.

We also used a pseudorandom generator function to select the embedding

locations of the integer wavelet coefficients to increase the system security. The

remaining of the paper will be organized as follows. Firstly, we will provide abrief introduction to integer wavelet transform. Secondly we will describe the

proposed steganographic system. Then, we will discuss the achieved results;

and finally we will conclude the paper and suggest future improvements to the

system.

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1.2 Block Diagram:

1.3 FUNDAMENTALS OF DIGITAL IMAGE

Digital image is defined as a two dimensional function f(x, y), where x

and y are spatial (plane) coordinates, and the amplitude of f at any pair of

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coordinates (x, y) is called intensity or grey level of the image at that point.

The field of digital image processing refers to processing digital images by

means of a digital computer. The digital image is composed of a finite number

of elements, each of which has a particular location and value. The elements are

referred to as picture elements, image elements, pels, and pixels. Pixel is the

term most widely used.

1.3.1Image Compression

Digital Image compression addresses the problem of reducing the amount

of data required to represent a digital image. The underlying basis of the

reduction process is removal of redundant data. From the mathematical

viewpoint, this amounts to transforming a 2D pixel array into a statically

uncorrelated data set. The data redundancy is not an abstract concept but a

mathematically quantifiable entity. If n1 and n2 denote the number of

information-carrying units in two data sets that represent the same information,

the relative data redundancy DR [2] of the first data set (the one characterized

by n1) can be defined as,

R

D

CR

11=

Where RC called as compression ratio [2]. It is defined as

RC =2

1

n

n

In image compression, three basic data redundancies can be identified

and exploited: Coding redundancy, interpixel redundancy, and phychovisal

redundancy. Image compression is achieved when one or more of these

redundancies are reduced or eliminated.

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The image compression is mainly used for image transmission and

storage. Image transmission applications are in broadcast television; remote

sensing via satellite, air-craft, radar, or sonar; teleconferencing; computer

communications; and facsimile transmission. Image storage is required most

commonly for educational and business documents, medical images that arise in

computer tomography (CT), magnetic resonance imaging (MRI) and digital

radiology, motion pictures, satellite images, weather maps, geological surveys,

and so on.

1.3.2 Image Compression Model

image compressed

image

Figure 1.1.a) Block Diagram of Image compression

Compressed Reconstructed

image image

Figure 1.1.b) Block Diagram of Image Decompression

1.3.3 Image Compression Types

There are two types image compression techniques.

1. Lossy Image compression

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Forward

Transform

Encod

er

InverseDecoder


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2. Lossless Image compression

Compression ratio:

1. Lossy Image compression :

Lossy compression provides higher levels of data reduction but result in a

less than perfect reproduction of the original image. It provides high

compression ratio. lossy image compression is useful in applications such as

broadcast television, videoconferencing, and facsimile transmission, in which acertain amount of error is an acceptable trade-off for increased compression

performance.

Originally, PGF has been designed to quickly and progressively decode

lossy compressed aerial images. A lossy compression mode has been preferred,

because in an application like a terrain explorer texture data (e.g., aerial

orthophotos) is usually mid-mapped filtered and therefore lossy

mapped onto the terrain surface. In addition, decoding lossy compressed images

is usually faster than decoding lossless compressed images.

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In the next test series we evaluate the lossy compression efficiency of PGF. One

of the best competitors in this area is for sure JPEG 2000. Since JPEG 2000 has

two different filters, we used the one with the better trade-off between

compression efficiency and runtime. On our machine the 5/3 filter set has a

better trade-off than the other. However, JPEG 2000 has in both cases a

remarkable good compression efficiency for very high compression ratios but

also a very poor encoding and decoding speed.

The other competitor is JPEG. JPEG is one of the most popular image fileformats. It is very fast and has a reasonably good compression efficiency for a

wide range of compression ratios. The drawbacks of JPEG are the missing

lossless compression and the often missing progressive decoding. Fig. 4 depicts

the average rate-distortion behavior for the images in the Kodak test set when

fixed (i.e., nonprogressive) lossy compression is used. The PSNR of PGF is on

average 3% smaller than the PSNR of JPEG 2000, but 3% better than JPEG.

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These results are also qualitative valid for our PGF test set and they are

characteristic for aerial ortho-photos and natural images. Because of the design

of PGF we already know that PGF does not reach the compression efficiency of

JPEG 2000. However, we are interested in the trade-off between compression

efficiency and runtime. To report this trade-off we show in Table 4 a

comparison between JPEG 2000 and PGF and in Fig. 5 (on page 8) we show for

the same test series as in Fig. 4 the corresponding average decoding times in

relation to compression ratios.

Table 4 contains for seven different compression ratios (mean values over the

compression ratios of the eight images of the Kodak test set) the corresponding

average encoding and decoding times in relation to the average PSNR values. In

case of PGF the encoding time is always slightly longer than the corresponding

decoding time. The reason for that is that the actual encoding phase (cf.Subsection 2.4.2) takes slightly longer than the corresponding decoding phase.

For six of seven ratios the PSNR difference between JPEG 2000 and PGF is

within 3% of the PSNR of JPEG 2000. Only in the first row is the difference

larger (21%), but because a PSNR of 50 corresponds to an almost perfect image

quality the large PSNR difference corresponds with an almost undiscoverablevisual difference. The price they pay in JPEG 2000 for the 3% more PSNR is

very high. The creation of a PGF is five to twenty times faster than the creation

of a corresponding JPEG 2000 file, and the decoding of the created PGF is still

five to ten times faster than the decoding of the JPEG 2000 file. This gain in

speed is remarkable, especially in areas where time is more important than

quality, maybe for instance in real-time computation.

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In Fig. 5 we see that the price we pay in PGF for the 3% more PSNR than JPEG

is low: for small compression ratios (< 9) decoding in PGF takes two times

longer than JPEG and for higher compression ratios (> 30) it takes only ten

percent longer than JPEG. These test results are characteristic

for both natural images and aerial ortho-photos. Again, in the third test series

we only use the Lena image. We run our lossy coder with six different

quantization parameters and measure the PSNR in relation to the resulting

compression ratios. The results (ratio: PSNR) are:

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2.Lossless Image compression :

Lossless Image compression is the only acceptable amount of data

reduction. It provides low compression ratio while compared to lossy. In

Lossless Image compression techniques are composed of two relatively

independent operations: (1) devising an alternative representation of the image

in which its interpixel redundancies are reduced and (2) coding the

representation to eliminate coding redundancies.

Lossless Image compression is useful in applications such as medical

imaginary, business documents and satellite images.

Table 2 summarizes the lossless compression efficiency and Table 3 the codingtimes of the PGF test set. For WinZip we only provide average runtime values,

because of missing source code we have to use an interactive testing procedure

with runtimes measured by hand. All other values are measured in batch mode.

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In Table 2 it can be seen that in almost all cases the best compression ratio is

obtained by JPEG 2000, followed by PGF, JPEG-LS, and PNG. This result is

different to the result in [SEA+00], where the best performance for a similar test

set has been reported for JPEG-LS. PGF performs between 0.5% (woman) and

21.3% (logo) worse than JPEG 2000. On average it is almost 15% worse. The

two exceptions to the general trend are the compound and the logo images.

Both images contain for the most part black text on a white background. For

this type of images, JPEG-LS and in particular WinZip and PNG provide much

larger compression ratios. However, in average PNG performs the best, which is

also reported in [SEA+00].

These results show, that as far as lossless compression is concerned, PGF

performs reasonably well on natural and aerial images. In specific types of

images such as compound and logo PGF is outperformed by far in PNG.

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Table 3 shows the encoding (enc) and decoding (dec) times (measured in

seconds) for the same algorithms and images as in Table 2. JPEG 2000 and PGF

are both symmetric algorithms, while WinZip, JPEG-LS and in particular PNG

are asymmetric with a clearly shorter decoding than encoding time. JPEG 2000,

the slowest in encoding and decoding, takes more than four times longer than

PGF. This speed gain is due to the simpler coding phase of PGF. JPEG-LS is

slightly slower than PGF during encoding, but slightly faster in decoding

images.

WinZip and PNG decode even more faster than JPEG-LS, but their

encoding times are also worse. PGF seems to be the best compromise between

encoding and decoding times. Our PGF test set clearly shows that PGF in

lossless mode is best suited for natural images and aerial orthophotos. PGF is

the only algorithm that encodes the three MByte large aerial ortho-photo in less

than second without a real loss of compression efficiency. For this particular

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image the efficiency loss is less than three percent compared to the best. These

results should be underlined with our second test set, the Kodak test set.

Fig. 3 shows the averages of the compression ratios (ratio), encoding

(enc), and decoding (dec) times over all eight images. JPEG 2000 shows in thistest set the best compression efficiency followed by PGF, JPEG-LS, PNG, and

WinZip. In average PGF is eight percent worse than JPEG 2000. The fact that

JPEG 2000 has a better lossless compression ratio than PGF does not surprise,

because JPEG 2000 is more quality driven than PGF.

However, it is remarkable that PGF is clearly better than JPEG-LS

(+21%) and PNG (+23%) for natural images. JPEG-LS shows in the Kodak test

set also a symmetric encoding and decoding time behavior. Its encoding and

decoding times are almost equal to PGF. Only PNG and WinZip can faster

decode than PGF, but they also take longer than PGF to encode.

If both compression efficiency and runtime is important, then PGF is clearly the

best of the tested algorithms for lossless compression of natural images and

aerial orthophotos. In the third test we perform our lossless coder on the Lena

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image. The compression ratio is 1.68 and the encoding and decoding takes 0.25

and 0.19 seconds, respectively.

1.4.4. Image Compression Standards

There are many methods available for lossy and lossless, image

compression. The efficiency of these coding standardized by some

Organizations. The International Standardization Organization (ISO) and

Consultative Committee of the International Telephone and Telegraph (CCITT)are defined the image compression standards for both binary and continuous

tone (monochrome and Colour) images. Some of the Image Compression

Standards are

1. JBIG1

2. JBIG2

3. JPEG-LS

4. DCT based JPEG

5. Wavelet based JPEG2000

Currently, JPEG2000 [3] is widely used because; the JPEG-2000 standard

supports lossy and lossless compression of single-component (e.g., grayscale)

and multicomponent (e.g., color) imagery. In addition to this basic compression

functionality, however, numerous other features are provided, including: 1)

progressive recovery of an image by fidelity or resolution; 2) region of interest

coding, whereby different parts of an image can be coded with differing fidelity;

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3) random access to particular regions of an image without the needed to decode

the entire code stream; 4) a flexible file format with provisions for specifying

opacity information and image sequences; and 5) good error resilience. Due to

its excellent coding performance and many attractive features, JPEG 2000 has a

very large potential application base. Some possible application areas include:

image archiving, Internet, web browsing, document imaging, digital

photography, medical imaging, remote sensing, and desktop publishing.

The main advantage of JPEG2000 over other standards, First, it would

addresses a number of weaknesses in the existing JPEG standard. Second, it

would provide a number of new features not available in the JPEG standard.

The preceding points led to several key objectives for the new standard,

namely that it should: 1) allow efficient lossy and lossless compression within a

single unified coding framework, 2) provide superior image quality, both

objectively and subjectively, at low bit rates, 3) support additional features such

as region of interest coding, and a more flexible file format, 4) avoid excessive

computational and memory complexity. Undoubtedly, much of the success of

the original JPEG standard can be attributed to its royalty-free nature.

Consequently, considerable effort has been made to ensure that minimally-

compliant JPEG- 2000 codec can be implemented free of royalties.

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CHAPTER 2

2.1. INTRODUCTION TO WAVELET::

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Over the past several years, the wavelet transform has gained widespread

acceptance in signal processing in general and in image compression research in

particular. In applications such as still image compression, discrete wavelets

transform (DWT) based schemes have outperformed other coding schemes like

the ones based on DCT. Since there is no need to divide the input image into

non-overlapping 2-D blocks and its basis functions have variable length,

wavelet-coding schemes at higher compression ratios avoid blocking artifacts.

Because of their inherent multiresolution nature, wavelet-coding schemes are

especially suitable for applications where scalability and tolerable degradation

are important. Recently the JPEG committee has released its new image coding

standard, JPEG-2000, which has been based upon DWT.

Basically we use Wavelet Transform (WT) to analyze non-stationary

signals, i.e., signals whose frequency response varies in time, as Fourier

Transform (FT) is not suitable for such signals.

To overcome the limitation of FT, Short Time Fourier Transform (STFT)

was proposed. There is only a minor difference between STFT and FT. In

STFT, the signal is divided into small segments, where these segments

(portions) of the signal can be assumed to be stationary. For this purpose, a

window function "w" is chosen. The width of this window in time must be

equal to the segment of the signal where it is still be considered stationary. By

STFT, one can get time-frequency response of a signal simultaneously, whichcant be obtained by FT. The short time Fourier transform for a real continuous

signal is defined as:

X (f, t) =

dtetwtx ftj 2* ])()([ ------------ (2.1)

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Where the length of the window is (t-) in time such that we can shift the

window by changing value of t, and by varying the value we get different

frequency response of the signal segments.

The Heisenberg uncertainty principle explains the problem with STFT.

This principle states that one cannot know the exact time-frequency

representation of a signal, i.e., one cannot know what spectral components exist

at what instances of times. What one canknow are the timeintervalsin which

certain band of frequencies exists and is called resolution problem. This

problem has to do with the widthof the window function that is used, known asthesupportof the window. If the window function is narrow, then it is known

as compactly supported. The narrower we make the window, the better the time

resolution, and better the assumption of the signal to be stationary, but poorer

the frequency resolution:

Narrow window ===> good time resolution, poor frequency resolution

Wide window ===> good frequency resolution, poor time resolution

The wavelet transform (WT) has been developed as an alternate approach

to STFT to overcome the resolution problem. The wavelet analysis is done such

that the signal is multiplied with the wavelet function, similar to the window

function in the STFT, and the transform is computed separately for different

segments of the time-domain signal at different frequencies. This approach iscalled Multiresolution Analysis (MRA) [4], as it analyzes the signal at different

frequencies giving different resolutions.

MRA is designed to give good time resolution and poor frequency

resolution at high frequencies and good frequency resolution and poor time

resolution at low frequencies. This approach is good especially when the signal

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has high frequency components for short durations and low frequency

components for long durations, e.g., images and video frames.

The wavelet transform involves projecting a signal onto a complete set oftranslated and dilated versions of a mother wavelet (t). The strict definition of

a mother wavelet will be dealt with later so that the form of the wavelet

transform can be examined first. For now, assume the loose requirement that

(t) has compact temporal and spectral support (limited by the uncertainty

principle of course), upon which set of basis functions can be defined.

The basis set of wavelets is generated from the mother or basic wavelet is

defined as:

a,b(t) =

a

bt

a

1; a, b and a>0 ------------ (2.2)

The variable a (inverse of frequency) reflects the scale (width) of a

particular basis function such that its large value gives low frequencies and

small value gives high frequencies. The variable b specifies its translation

along x-axis in time. The term 1/ a is used for normalization.

2.2. WAVELET TRANSFORM

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Whether we like it or not we are living in a world of signals. Nature is

talking to us with signals: light, sounds Men are talking to each other with

signals: music, TV, phones

The human body is equipped to survive in this world of signals with

sensors such as eyes and ears, which are able to receive and process these

signals. Consider, for instance, our ears: they can discriminate the volume and

tone of a voice. Most of the information our ears process from a signal is in the

frequency content of the signal.

Scientists have developed mathematical methods to imitate the processingperformed by our body and extract the frequency information contained in a

signal. These mathematical algorithms are called transforms and the most

popular among them is the Fourier Transform.

The second method to analyze non-stationary signals is to first filter

different frequency bands, cut these bands into slices in time, and then analyze

them.

The wavelet transform uses this approach. The wavelet transform or

wavelet analysis is probably the most recent solution to overcome the

shortcomings of the Fourier transform. In wavelet analysis the use of a fully

scalable modulated window solves the signal-cutting problem. The window is

shifted along the signal and for every position the spectrum is calculated.

Thenthis process is repeated many times with a slightly shorter (or longer)

window for every new cycle.

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In the end the result is a collection of time-frequency representations of

the signal, all with different resolutions. Because of this collection of

representations, we can speak of a multiresolution analysis. In the case of

wavelets, we normally do not speak about time-frequency

Discrete Wavelet Transform

The discrete wavelet transform (DWT) was developed to apply the

wavelet transform to the digital world. Filter banks are used to approximate the

behavior of the continuous wavelet transform. The signal is decomposed with a

high-pass filter and a low-pass filter. The coefficients of these filters are

computed using mathematical analysis and made available to you. See

Appendix B for more information about these computations.

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Where

LPd: Low Pass Decomposition Filter

HPd: High Pass Decomposition Filter

LPr: Low Pass Reconstruction Filter

HPr: High Pass Reconstruction Filter

The wavelet literature presents the filter coefficients to you in tables. An

example is the Daubechies filters for wavelets. These filters depend on a

parameterp called the vanishing

moment.

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The hp[n] coefficients are used as the low-pass reconstruction filter (LPr).

The coefficients for the filters HPd, LPd and HPr are computed from the h[n]

coefficients as follows:

High-pass decomposition filter (HPd) coefficients

g[n] = (1)n h[Ln] (L: length of the filter)

Low-pass reconstruction filter (LPr) coefficients

h[n] = h[Ln] (L: length of the filter)

High-pass reconstruction filter (HPr) coefficients

g[n] = g[Ln] (L: length of the filter)

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The Daubechies filters for Wavelets are provided in the C55x IMGLIB for

2 p 10. Since there are several sets of filters, we may ask ourselves what are

the advantages and disadvantages to using one set or another.

First we need to understand that we will have perfect reconstruction no

matter what the filter length is. However, longer filters provide smoother,

smaller intermediate results. Thus, if intermediate processing is required, we are

less likely to lose information due to necessary threshold or saturation.

However, longer filters obviously involve more processing.

Wavelets and Perfect Reconstruction Filter Banks

Filter banks decompose the signal into high- and low-frequency

components. The low-frequency component usually contains most of the

frequency of the signal. This is called the approximation. The high-frequency

component contains the details of the signal.

Wavelet decomposition can be implemented using a two-channel filter

bank. Two-channel filter banks are discussed in this section briefly. The main

idea is that perfect reconstruction filter banks implement series expansions of

discrete-time signals.

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The input and the reconstruction are identical; this is called perfect

reconstruction. Two popular decomposition structures arepyramidand wavelet

packet. The first one decomposes only the approximation (low-frequency

component) part while the second one decomposes both the

approximation and the detail (high-frequency component).

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Figure 8. Wavelet Packet Decomposition

The C55x IMGLIB provides the following functions for one dimension

pyramid and packet decomposition and reconstruction. Complete information

about these functions can be found in

the C55x IMGLIB.

1-D discrete wavelet transform

void IMG_wave_decom_one_dim(short *in_data, short *wksp, int *wavename,

int length,int level);

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1-D inverse discrete wavelet transform

void IMG_wave_recon_one_dim(short *in_data, short *wksp, int *wavename,


1-D discrete wavelet package transform

void IMG_wavep_decom_one_dim(short *in_data, short *wksp, int

*wavename, int length,int level);

1-D inverse discrete wavelet package transform

void IMG_wavep_recon_one_dim(short *in_data, short *wksp, int *wavename,


Wavelets Image Processing

Wavelets have found a large variety of applications in the image

processing field. The JPEG 2000 standard uses wavelets for image compression.

Other image processing applications such as noise reduction, edge detection,

and finger print analysis have also been investigated in the literature.

Wavelet Decomposition of Images

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In wavelet decomposing of an image, the decomposition is done row by

row and then column by column. For instance, here is the procedure for an N x

M image. You filter each row and then down-sample to obtain two N x (M/2)

images. Then filter each column and subsample the filter output to obtain four

(N/2) x (M/2) images.

Of the four subimages obtained as seen in Figure 12, the one obtained by

low-pass filtering the rows and columns is referred to as the LL image.

The one obtained by low-pass filtering the rows and high-pass filtering the

columns is referred to as the LH images. The one obtained by high-pass filtering

the rows and low-pass filtering the columns is called the HL image. The

subimage obtained by high-pass filtering the rows and columns is referred to as

the HH image. Each of the subimages obtained in this fashion can then be

filtered and subsampled to obtain four more subimages. This process can be

continued until the desired subband structure is

obtained.

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Three of the most popular ways to decompose an image are: pyramid, spacl, and

wavelet packet, as shown in Figure 13.

In the structure of pyramid decomposition, only the LL subimage is

decomposed after each decomposition into four more subimages.

In the structure of wavelet packet decomposition, each subimage(LL, LH,HL,

HH) is decomposed after each decomposition.

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In the structure of spacl, after the first level of decomposition, each subimage

is decomposed into smaller subimages, and then only the LL subimage is

decomposed.

Figure14 shows a three-level decomposition image of pyramid structure.

In the part I development stage, the JPEG 2000 standard supports the

pyramid decomposition structure. In the future all three structures will be

supported.

For two dimensions, the C55x IMGLIB provides functions for pyramid and

packet decomposition and reconstruction. Complete information about these

functions can be found in the C55x IMGLIB.

2-D discrete wavelet transform

void IMG_wave_decom_two_dim(short **image, short * wksp, int width, int

height, int *wavename, int level);

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2-D inverse discrete wavelet transform

void IMG_wave_recon_two_dim(short **image, short * wksp, int width, int


2-D discrete wavelet package transform

void IMG_wavep_decom_two_dim(short **image, short * wksp, int width, int


2-D inverse discrete wavelet package transform

void IMG_wavep_recon_two_dim(short **image, short * wksp, int width, int


Wavelets Applications

TI provides several one dimension and two dimension wavelets

applications, which illustrate how to use the wavelets functions provided in the

C55x IMGLIB.

2.2.1. 1-D Continuous wavelet transform

The 1-D continuous wavelet transform is given by:

Wf(a, b) =

dtttxba

)()( , ------------ (2.3)

The inverse 1-D wavelet transform is given by:

x (t) =

02,

)(),(1

a

dadbtbaW

Cbaf ------------ (2.4)

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Where C =

d

2)

<

( ) is the Fourier transform of the mother wavelet (t). Cis required

to be finite, which leads to one of the required properties of a mother wavelet.

Since Cmust be finite, then 0)0( = to avoid a singularity in the integral, and

thus the )(t must have zero mean. This condition can be stated as

dtt)( = 0 and known as the admissibility condition.

2.2.2. 1-D Discrete wavelet transform

The discrete wavelets transform (DWT), which transforms a discrete time

signal to a discrete wavelet representation. The first step is to discretize the

wavelet parameters, which reduce the previously continuous basis set of

wavelets to a discrete and orthogonal / orthonormal set of basis wavelets.

m,n(t) = 2m/2(2mt n) ; m, n such that - < m, n < -------- (2.5)

The 1-D DWT is given as the inner product of the signal x(t) being

transformed with each of the discrete basis functions.

Wm,n = < x(t), m,n(t) > ; m, n Z ------------ (2.6)

The 1-D inverse DWT is given as:

x (t) = m n

nmnm tW )(,, ; m, n Z ------------- (2.7)

One Dimension Wavelet Applications

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The 1D_Demo.c file presents applications of the one-dimension wavelet.

A 128-point sine wave

is used as input for all these applications as shown in Figure 15:

1-D Perfect Decomposition and Reconstruction Example

The third application shows a three-level pyramid decomposition and

reconstruction of the input signal:

// Perfect Reconstruction of Pyramid, Level 3

//==================================================

for( i = 0; i < LENGTH; i++ )

signal[i] = backup[i];

IMG_wave_decom_one_dim( signal, temp_wksp, db4, LENGTH, 3 );

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IMG_wave_recon_one_dim( signal, temp_wksp, db4, LENGTH, 3 );

for( i = 0; i < LENGTH; i++ )

noise[i] = signal[i] backup[i];

//

The error signal shown in Figure 24 represents the difference between the

original signal and the reconstructed signal. This error signal is not zero becauseof the dynamic range of the 16-bit fixed-point data.

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2.2.3. 2-D wavelet transform

The 1-D DWT can be extended to 2-D transform using separable wavelet

filters. With separable filters, applying a 1-D transform to all the rows of the

input and then repeating on all of the columns can compute the 2-D transform.

When one-level 2-D DWT is applied to an image, four transform coefficient

sets are created. As depicted in Figure 2.1(c), the four sets are LL, HL, LH, and

HH, where the first letter corresponds to applying either a low pass or high pass

filter to the rows, and the second letter refers to the filter applied to the columns.

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Figure 2.1. Block Diagram of DWT (a)Original Image (b) Output image after

the 1-D applied on Row input (c) Output image after the second 1-D applied on

row input

Figure 2.2. DWT for Lena image (a)Original Image (b) Output image

after the 1-D applied on column input (c) Output image after the second 1-D

applied on row input

The Two-Dimensional DWT (2D-DWT) converts images from spatial

domain to frequency domain. At each level of the wavelet decomposition, each

column of an image is first transformed using a 1D vertical analysis filter-bank.

The same filter-bank is then applied horizontally to each row of the filtered and

subsampled data. One-level of wavelet decomposition produces four filtered

and subsampled images, referred to as subbands. The upper and lower areas of

Fig. 2.2(b),respectively, represent the low pass and high pass coefficients aftervertical 1D-DWT and sub sampling. The result of the horizontal 1D-DWT and

sub sampling to form a 2D-DWT output image is shown in Fig.2.2(c).

We can use multiple levels of wavelet transforms to concentrate data

energy in the lowest sampled bands. Specifically, the LL subband in fig 2.1(c)

can be transformed again to form LL2, HL2, LH2, and HH2 subbands,

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producing a two-level wavelet transform. An (R-1) level wavelet decomposition

is associated with R resolution levels numbered from 0 to (R-1), with 0 and (R-

1) corresponding to the coarsest and finest resolutions.

The straight forward convolution implementation of 1D-DWT requires a

large amount of memory and large computation complexity. An alternative

implementation of the 1D-DWT, known as the lifting scheme, provides

significant reduction in the memory and the computation complexity. Lifting

also allows in-place computation of the wavelet coefficients. Nevertheless, the

lifting approach computes the same coefficients as the direct filter-bank

convolution.

Two Dimension Wavelet Applications

The 2D_Demo.c file, provided in the C55x IMGLIB, presentsapplications of the two-dimension wavelet. A 128x128 image is used as input

for all these applications. In the first application we are using the picture in

Figure 25:

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2-D Perfect Decomposition and Reconstruction Example

In this application, the image is one-level decomposed and reconstructed.

You notice no difference between the original picture and the reconstructed

picture as shown in Figure 26.

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Edge Detection Example

In the second application, a 2-D edge detection is performed for the

picture in Figure 27:

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The HH part of the picture has a vertical line. This happens because a row by

row processing was performed first and then a column by column.

2.3. LIFTING SCHEME

The wavelet transform of image is implemented using the lifting scheme

[5]. The lifting operation consists of three steps. First, the input signal x[n] is

down sampled into the even position signal xe (n) and the odd position signalxo(n) , then modifying these values using alternating prediction and updating

steps.

xe (n) = x [2n] and xo(n) = x [2n+1] ------------- (2.8)

A prediction step consists of predicting each odd sample as a linear

combination of the even samples and subtracting it from the odd sample to form

the prediction error. An update step consists of updating the even samples by

adding them to a linear combination of the prediction error to form the updated

sequence. The prediction and update may be evaluated in several steps until the

forward transform is completed. The block diagram of forward lifting and

inverse lifting is shown in figure 2.3.

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xe (n) s

x (n)

xo(n) d

(a)

s

x (n)

d

(b)

Figure 2.3 The Lifting Scheme. (a) Forward Transform (b) Inverse

Transform

The inverse transform is similar to forward. It is based on the three

operations undo update, undo prediction, and merge. The simple lifting

technique using Haar wavelet is explained in next section.

2.4. LIFTING USING HARR

The lifting scheme is a useful way of looking at discrete wavelet

transform. It is easy to understand, since it performs all operations in the time

domain, rather than in the frequency domain, and has other advantages as well.

This section illustrates the lifting approach using the Haar Transform [6].

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Split UP

MergeU P


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The Haar transform is based on the calculations of the averages

(approximation co-efficient) and differences (detail co-efficient). Given two

adjacent pixels a and b, the principle is to calculate the average 2

)( bas

+=

and

the difference bad = . If a and b are similar, s will be similar to both and d will

be small, i.e., require few bits to represent. This transform is reversible, since

2

dsa = and

2

dsb += and it can be written using matrix notation as

=

2/1

2/1),(),( bads

1

1= (a,b)A,

=2/1

1),(),( dsba

2/1

1= 1),( Ads

Consider a row of n2 pixels values lnS , for nl 20


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CHAPTER 3

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3.1 Introduction to LSB:

Data hiding is a method of hiding secret messages into a cover-media

such that an unintended observer will not be aware of the existence of thehidden messages. In this paper, 8-bit grayscale images are selected as the

covermedia. These images are called cover-images. Cover-images with the

secret messages embedded in them are called stego-images. For data hiding

methods, the image quality refers to the quality of the stego-images.

In the literature, many techniques about data hiding have been proposed.

One of the common techniques isbased on manipulating the least-signi7cant-bit

(LSB) planesby directly replacing the LSBs of the cover-image with the

message bits. LSB methods typically achieve high capacity.Wang et al.

proposed to embed secret messages in themoderately significant bit of the

cover-image. A genetic algorithmis developed to 7nd an optimal substitution

matrixfor the embedding of the secret messages.

They also proposedto use a local pixel adjustment process (LPAP) to

improve the image quality of the stego-image. Unfortunately, since the local

pixel adjustment process only considers the last three least significant bits and

the fourth bit but not on all bits, the local pixel adjustment process is obviously

not optimal. The weakness of the local pixel adjustment process is pointed out

in Ref. As the local pixel adjustment process modifies the LSBs, the technique

cannot be applied to data hiding schemes based on simple LSB substitution.

Recently, Wang et al. further proposed a data hiding scheme by optimal LSB

substitution and genetic algorithm. Using the proposed algorithm, the worst

mean-square-error (WMSE) between the cover-image and the stego-image is

shown to be 1/2 of that obtained by the simple LSB substitution method.

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In this paper, a data hiding scheme by simple LSB substitution with an

optimal pixel adjustment process (OPAP) is proposed. The basic concept of the

OPAP is based on the technique proposed. The operations of the OPAP are

generalized. The WMSE between the cover-image and the stego-image is

derived. It is shown that the WMSE obtained by the OPAP could be less than

of that obtained by the simple LSB substitution method. Experimental results

demonstrate that enhanced image quality can be obtained with low extra

computational complexity. The results obtained also show better performance

than the optimal substitution method described.

3.2 Data hiding by simple LSB substitution:

In this section, the general operations of data hiding by simple LSB

substitution method are described.

Let C be the original 8-bit grayscale cover-image of Mc Nc pixels represented

as

M be the n-bit secret message represented as

Suppose that the n-bit secret message M is to be embedded into the k-rightmost

LSBs of the cover-image C. Firstly, the secret message M is rearranged to form

a conceptually k-bit virtual image M_represented as

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Where The mapping between the n-bit secret message.

And the embedded message can be defined as follows:

Secondly, a subset of n_pixels {xl1; xl2 ,.. xln_ } is chosen from the cover-

image C in a predefined sequence. The embedding process is completed by

replacing the k LSBs of xli by mi . Mathematically, the pixel value xli of the

chosen pixel for storing the k-bit message mi is modified to form the stego-

pixel xli as follows:

In the extraction process, given the stego-image S, the embedded messages can

be readily extracted without referring to the original cover-image. Using the

same sequence as in the embedding process, the set of pixels{xl1, xl2,.

Xln} storing the secret message bits are selected from the stego-image. The k

LSBs of the selected pixels are extracted and lined up to reconstruct the secret

message bits. Mathematically, the embedded message bits mi can be recovered

by

Suppose that all the pixels in the cover-image are used for the embedding of

secret message by the simple LSB substitution method. Theoretically, in the

worst case, the

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PSNR of the obtained stego-image can be computed by

Table 1 tabulates the worst PSNR for some k = 15. It could be seen that the

image quality of the stego-image is degraded drastically when k>4.

3.3 Optimal pixel adjustment process:

In this section, an optimal pixel adjustment process (OPAP) is proposed

to enhance the image quality of the stego-image obtained by the simple LSB

substitution method. The basic concept of the OPAP is based on the technique

proposed.

Let pi , pi and pi be the corresponding pixel values of the ith pixel in the

cover-image C, the stego-image Cobtained by the simple LSB substitution

method and the refined stego-image obtained after the OPAP. Let

be the embedding error between pi and pi . According to the embedding

process of the simple LSB substitution method described in Section 2, pi is

obtained by the direct replacement of the k least signi7cant bits of pi with k

message bits, therefore,

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The value of can be further segmented into three intervals, such that

Based on the three intervals, the OPAP, which modifi7es pi to form the stego-

pixel pi, can be described as follows:

Let be the embedding error between pi and pi. can be

computed as follows:

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From the above 7ve cases, it can be seen that the absolute value of may fall

into the range only when and

( case 5);while for other possible values of falls into the

range , because is obtained by the direct replacement of the

k lab of Pi with the message bits are equivalent

to Pi256-2^k, respectively in general for gray scale natural

images, when k


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Let WMSE and WMSE be the worst case mean-squareerror between the

stego-image and the cover-image obtained by the simple LSB substitution

method and the proposed method with OPAP, respectively. WMSE* can be

derived by

reveals that WMSE*< WMSE, for k>2; and WMSE* WMSE

when k=4. This result also shows that the WMSE*obtained by the OPAP is

better than that obtained by the optimal substitution method proposed in which

WMSE*= WMSE.

Moreover, the optimal pixel adjustment process only requires a checking

of the embedding error between the original cover-image and the stego-image

obtained by the simple LSB substitution method to form the final stego-image.

The extra computational cost is very small compared with Wangs method

which requires huge computation for the genetic algorithm to 7nd an optimal

substitution matrix.

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CHAPTER 4

4.1 Introduction to Matlab:

The tutorials are independent of the rest of the document. The primarily

objective is to help you learn quickly the rst steps. The emphasis here is

learning by doing". Therefore, the best way to learn is by trying it yourself.

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Working through the examples will give you a feel for the way that MATLAB

operates. In this introduction we will describe how MATLAB handles simple

numerical expressions and mathematical formulas.

The name MATLAB stands for MATrix LABoratory. MATLAB was

written originally to provide easy access to matrix software developed by the

LINPACK (linear system package) and EISPACK (Eigen system package)

projects. MATLAB is a high-performance language for technical computing. It

integrates computation, visualization, andprogrammingenvironment.

Furthermore, MATLAB is a modern programming language environment: it has

sophisticated data structures, contains built-in editing and debugging tools, and

supports object-oriented programming. These factors make MATLAB an

excellent tool for teaching and research.

MATLAB has many advantages compared to conventional computer

languages (e.g., C, FORTRAN) for solving technical problems. MATLAB is an

interactive system whose basic data element is an array that does not requiredimensioning. The software package has been commercially available since

1984 and is now considered as a standard tool at most universities and

industries worldwide. It has powerful built-in routines that enable a very wide

variety of computations. It also has easy to use graphics commands that make

the visualization of results immediately

available. Specic applications are collected in packages referred to as toolbox.

There are toolboxes for signal processing, symbolic computation, control

theory, simulation, optimiza-tion, and several other fields of applied science and

engineering.

Basic features

As we mentioned earlier, the following tutorial lessons are designed to get

you started quickly in MATLAB. The lessons are intended to make you familiar61


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with the basics of MATLAB. We urge you to complete the exercises given at

the end of each lesson.

4.2 Starting MATLAB

After logging into your account, you can enter MATLAB by double-

clicking on the MATLAB shortcut icon (MATLAB 7.0.4) on your Windows

desktop. When you start MATLAB, a special window called the MATLAB

desktop appears. The desktop is a window that contains otherwindows. The

major tools within or accessible from the desktop are:

The Command Window

The Command History

The Workspace

The Current Directory

The Help Browser

The Start button

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Figure 1.1: The graphical interface to the MATLAB workspace

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Change the current working directory

Arithmetic operators

plus - Plus +

uplus - Unary plus +

minus - Minus -

uminus - Unary minus -

mtimes - Matrix multiply *

times - Array multiply .*

mpower - Matrix power ^

power - Array power .^

mldivide - Backslash or left matrix divide \

mrdivide - Slash or right matrix divide /

ldivide - Left array divide .\

rdivide - Right array divide ./

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Relational operators

eq - Equal ==

ne - Not equal ~= lt - Less than

le - Less than or equal =

Logical operators

Short-circuit logical AND &&

Short-circuit logical OR ||

and - Element-wise logical AND &

or - Element-wise logical OR |

not - Logical NOT ~

xor - Logical EXCLUSIVE OR

any - True if any element of vector is nonzero

Vectors

a = [1 2 3 4 5 6 9 8 7] ;

t = 0:2:20

t = 0 2 4 6 8 10 12 14 16 18 20

b = a + 2

b = 3 4 5 6 7 8 11 10 9

c = a + b

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c = 4 6 8 10 12 14 20 18 16

Matrices

B = [1 2 3 4;5 6 7 8;9 10 11 12] ;

B = 1 2 3 4

5 6 7 8

9 10 11 12

C = B'

C = 1 5 9

2 6 10

3 7 11

4 8 12

Plot

t=0:0.25:7;

y = sin(t);

plot(t,y)66


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t=0:0.25:7;

y = sin(t);

plot(t,y) ;

xlabel('x axis');

ylabel('y axis');

title('Heading');

grid on;

gtext('text');

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IF LOOP

if a > 6

disp('a is greater');

elseif a==0

disp('a is zero');

else

disp('a is smaller');

end

FOR LOOP

for i=1:5

a=a+1

end

disp(a);

While Loop

while a < 10

a=a+1;

end

disp(a);

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Function

function c=add(a,b); function c=mul(a,b);

c=a+b; c=a*b;

return return

Main

a=5;

b=6;

c=add(a,b);

disp(c);

d=mul(a,b);

disp(d);

SWITCH

a=input('enter---->');

switch a

case 1

fprintf('one');

case 2

fprintf('two');

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case 3

fprintf('three');

case 4

fprintf('four');

otherwise

fprintf('otherwise');

end

How to read an image

a =imread('cameraman.tif');

imshow(a);

pixval on;

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How to read an audio file

a =wavread('test.wav');

wavplay(a,44100);

Plot(a);

How to read an video file

a=aviread('movie.avi');

movie(a);

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Add two images

J = imread('cameraman.tif');

I = imread('rice.tif');

K = imadd(I,J');

imshow(K)

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Subtract two images

I = imread('rice.tif');

Iq = imsubtract(I,50);

subplot(1,2,1), imshow(I)

subplot(1,2,2), imshow(Iq)

Convert image to gray and binary

clc;

clear;

close all

a= imread('flowers.tif');

subplot(2,2,1);

imshow(a);

subplot(2,2,2);

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b=imresize(a,[256 256]);

imshow(b);

subplot(2,2,3);

c=rgb2gray(b);

imshow(c);

subplot(2,2,4);

d=im2bw(c);

imshow(d);

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RGB component

a=imread('flowers.tif');

subplot(2,2,1);

imshow(a);

R=a;

G=a;

B=a;

R(:,:,2:3)=0;

subplot(2,2,2);

imshow(R);

G(:,:,1)=0;

G(:,:,3)=0;

subplot(2,2,3);

imshow(G);

B(:,:,1)=0;

B(:,:,2)=0;

subplot(2,2,4);

imshow(B);

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CONVER MOVIE TO FRAMES

file=aviinfo('movie1.avi'); % to get inforamtaion abt video file

frm_cnt=file.NumFrames % No.of frames in the video file

str2='.bmp'

h = waitbar(0,'Please wait...');

for i=1:frm_cnt

frm(i)=aviread(filename,i); % read the Video file

frm_name=frame2im(frm(i)); % Convert Frame to image file

frm_name=rgb2gray(frm_name);%convert gray

filename1=strcat(strcat(num2str(i)),str2);

imwrite(frm_name,filename1); % Write image file

waitbar(i/frm_cnt,h)

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frm_cnt=5;

number_of_frames=frm_cnt;

filetype='.bmp';

display_time_of_frame=1;

mov = avifile('MOVIE.avi');

count=0;

for i=1:number_of_frames

name1=strcat(num2str(i),filetype);

a=imread(name1);

while count


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fid = fopen('message.txt','r');

ice1= fread(fid);

s = char(ice1');

fclose(fid);

disp(s);

Ans hello

How to write a text file

txt=[65 67 68 69];

fid = fopen('output.txt','wb'); fwrite(fid,char(txt),'char');

fclose(fid);

ANS =ACDE

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Store an Image,Audio


imwrite(a,'new.bmp');

a=wavread('test.wav');

wavwrite(d,44100,16,'nTEST.WAV');

Save and Load The Variable

A=5;

save A A;

load A

B=1;

C=A+B;

disp(C);

Wavelet transform

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[LL LH HL HH]=dwt2(a,'haar');

Dec=[...

LL,LH

HL,HH

...

];

imshow(Dec,[]);

DCT transform

a=imread('cameraman.tif');

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subplot(1,3,1);imshow(a,[]);

b=dct2(a);

subplot(1,3,2);imshow(b,[]);title('DCT');

c=idct2(b);

subplot(1,3,3);imshow(c,[]);title('IDCT');

NOISE AND FILTER

I = imread('eight.tif');

J = imnoise(I,'salt & pepper',0.02);

K = medfilt2(J);

subplot(1,2,1);imshow(J)

subplot(1,2,2);imshow(K)

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CHAPTER 5

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5.1 CONCLUSION:

In this paper we proposed a novel data hiding scheme that hides data into

the integer wavelet coefficients of an image. The system combines an adaptivedata hiding technique and the optimum pixel adjustment algorithm to increase

the hiding capacity of the system compared to other systems. The proposed

system embeds secret data in a random order using a secret key only known to

both sender and receiver.

It is an adaptive system which embeds different number of bits in each

wavelet coefficicient according to a hiding capacity function in order to

maximize the hiding capacity without sacrificing the visual quality of resulting

stego image. The proposed system also minimizes the difference between

original coefficients values and modified values by using the optimum pixel

adjustment algorithm.

The proposed scheme was classified into three cases of hiding capacity

according to different applications required by the user. Each case has different

visual quality of the stego-image. Any data type can be used as the secret

message since our experiments was made on a binary stream of data. There was

no error in the recovered message (perfect recovery) at any hiding rate. From

the experiments and the obtained results the proposed system proved to achieve

high hiding capacity up to 48% of the cover image size with reasonable image

quality and high security because of using random insertion of the secret

message. On the other hand the system suffers from low robustness against

various attacks such as histogram equalization and JPEG compression.

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The proposed system can be further developed to increase its robustness

by using some sort of error correction code which increases the probability of

retrieving the message after attacks, also investigating methods to increase

visual quality of the stego-image (PSNR) with the obtained hiding capacity.

5.2 REFERENCES:

[I) G. J. Simmons, "The prisoners' problern and the subliminal channel," in

Proceedings of Crypto' 83, pp. 51-67, 1984.

[2) N. Wu and M. Hwang. "Data Hiding: Current Status and Key Issues,"

International Journal of Network Security, Vol.4, No.1, pp. 1-9, Jan. 2007.

[3) W. Chen, "A Comparative Study of Information Hiding Schernes Using

Amplitude, Frequency and Phase Embedding," PhD Thesis, National Cheng

Kung University, Tainan, Taiwan, May 2003.

[4) C. Chan and L. M. Cheng, "Hiding data in images by simple LSB

substitution," Pattern Recognition, pp. 469-474, Mar. 2004.

[5) Changa, C. Changa, P. S. Huangb, and T. Tua, "A Novel bnage

Steganographic Method Using Tri-way Pixel-Value Differencing," Journal of

Multimedia, Vol. 3, No.2, June 2008.

[6) H. H. Zayed, "A High-Hiding Capacity Technique for Hiding Data in

images Based on K-Bit LSB Substitution," The 30th International Conference

on Artificial Intelligence Applications (ICAIA 2005) Cairo, Feb. 2005.

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[7) A. Westfeld, "F5a steganographic algorithm: High capacity despite better

steganalysis," 4th International Workshop on Information Hiding, pp.289-302,

April 25-27, 2001.

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