Compression and Denoising analysis from still images using Coiflets Wavelet Technique

Compression and Denoising Compression and Denoising

analysis from still images analysis from still images

using Coiflets Wavelet using Coiflets Wavelet

TechniqueTechnique

Presentation on……

ByB.B.S.KUMAR

Research Scholar, Asst. Prof., Dept. of ECE, Rajarajeswari College of Engineering,

Bangalore, India

National Conference at SJBIT

04-05-20131

SEMINAR OUTLINESEMINAR OUTLINE

�� IntroductionIntroduction

�� WaveletsWavelets

�� Coiflets WaveletCoiflets Wavelet

�� The Discrete Wavelet TransformThe Discrete Wavelet Transform�� The Discrete Wavelet TransformThe Discrete Wavelet Transform

�� Compression and DeCompression and De--noisingnoising

�� Experimental ResultsExperimental Results

�� Conclusion Conclusion

�� ReferencesReferencesNational Conference at SJBIT

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INTRODUCTIONINTRODUCTION

��ObjectiveObjective

• To investigate the still image compression and denoising of a

gray scale image using wavelet.

• Implemented in software using MATLAB version Wavelet

Toolbox and 2-D DWT technique.Toolbox and 2-D DWT technique.

• The main framework of this paper- compression and denoising

analysis from still images using Coiflets Wavelet Technique.


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�Work Approach

• The approach follows to know the Coiflets wavelet in image compression and denoising

• The experiments are conducted on still images(.jpg format)

• Image analysis using Coiflets wavelet remains the implementation of 2D DWT for still grey images

• The scope of the work involves–

– compression and de-noising

– image clarity

– to find the effect of the decomposition and threshold levels

– to find out energy retained (image recovery) and lost

– Reconstruction of image


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��Work LimitationWork Limitation

• It remains on the application side of wavelet theory and simulation

• The decomposition results depends on the choice of analyzing wavelet i.e., its corresponding filter that are analyzing wavelet i.e., its corresponding filter that are used.


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�� Problem DefinitionProblem Definition

• Each wavelet having efficient image clarity, but differs in

compression and de-noising percentage rate, hence this paper

presents Coiflets wavelet analysis at decomposition and

threshold levels.

• In this research the following basic classes of problems will be

considered – Image analysis, Image Reconstruction, Image

Compression and De-noising.Compression and De-noising.

• Wavelets in Image Processing

– Area of application- Wavelets work well for image compression

– problem -How small can we compress our data without losing vital

information?

– Area of application- Wavelet analysis lends itself well to denoising

images

– problem -What are essential features of the data, and what features are

“noise”?


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WAVELETWAVELET

��History of waveletsHistory of wavelets

• 1807 Joseph Fourier- theory of frequency analysis-- any 2pi functions f(x) is the sum of its Fourier Series

• 1909 Alfred Haar-- PhD thesis-- defined Haar basis function---- it is compact support( vanish outside finite interval) interval)

• 1930 Paul Levy-Physicist investigated Brownian motion ( random signal) and concluded Haar basis is better than FT

• 1930's Littlewood Paley, Stein ==> calculated the energy of the function 1960 Guido Weiss, Ronald Coifman--studied simplest element of functions space called atom.


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• 1980 Grossman (physicist) Moorlet( Engineer)-- broadly defined wavelet in terms of quantum mechanics

• 1985 Stephen Mallat--defined wavelet for his Digital Signal Processing work for his Ph.D.

• Y Meyer constructed first non trivial wavelet

• 1988 Ingrid Daubechies-- used Mallat work constructed set of

Cont…….

• 1988 Ingrid Daubechies-- used Mallat work constructed set of wavelets

• The name emerged from the literature of geophysics, by a route through France. The word onde led to ondelette. Translation wave led to wavelet

• What is an Wavelet ?-The Wavelets are functions that satisfy certain mathematical requirements and are used in representing data.


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��Disadvantages of FTDisadvantages of FT

• Dennis Gabor (1946) Used STFT

– To analyze only a small section of the signal at a time -- a

technique called Windowing the Signal.


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• Unchanged Window

• Dilemma of Resolution

– Narrow window : poor frequency resolution

– Wide window : poor time resolution

• Heisenberg Uncertainty Principle

– Cannot know what frequency exists at what time intervals

��Wavelet TransformWavelet Transform• Provides time-frequency representation

• Wavelet transform decomposes a signal into a set of basis functions (wavelets)

• Wavelets are obtained from a single prototype wavelet Ψ(t) called mother wavelet by dilations and shifting:

Ψa,b(t) =(1/√a) Ψ(t-b)/a – where a is the scaling parameter and b is the shifting parameter

• Wavelet analysis produces a time-scale view of the • Wavelet analysis produces a time-scale view of the signal.

– Scaling means stretching or compressing of the signal.

• The Good Transform Should be

– Decorrelate the image pixels

– Provide good energy compaction

– Desirable to be orthogonalNational Conference at SJBIT

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Sine waveSine wave WaveletWavelet db10db10

•The CWT is the sum over all time of the signal, multiplied by

scaled and shifted versions of the wavelet function


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• The oldest and simplest wavelet transform is based on the Haar scaling and wavelet functions

• Any discussion of wavelets begins with Haar wavelet, the first and simplest. Haar wavelet is discontinuous, and resembles a step function. It represents the same wavelet as

COIFLETS WAVELETCOIFLETS WAVELET

resembles a step function. It represents the same wavelet as Daubechies(db1)

• Coiflets (coif) : near symmetric, orthogonal, compact support and bi-orthogonal.

(Coiflets Built by I. Daubechies at the request of R. Coifman)


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Scaling function

Wavelet function Wavelet function


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��1D Discrete Wavelet Transform1D Discrete Wavelet Transform

• Separates the high and low-frequency portions of a signal through the use of filters

• One level of transform:– Signal is passed through G & H filters.

– Down sample by a factor of two

• Multiple levels (scales) are made by repeating the filtering and decimation process on lowpass outputs


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THE DISCRETE WAVELET THE DISCRETE WAVELET

TRANSFORMTRANSFORM• Separability, Scalability and Translatability

• Multiresolution Compatibility

• Orthogonality

– Provides sufficient information both for analysis and

synthesis

– Reduce the computation time sufficiently– Reduce the computation time sufficiently

– Easier to implement

– Analyze the signal at different frequency bands with

different resolutions

– Decompose the signal into a coarse approximation and detail

information


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� 22--D DWT processingD DWT processing

• Step 1: replace each row with its 1-D DWT.

• Step 2: Replace each column with its 1-D DWT

• Step 3: Repeat steps 1 & 2 on the lowest subband for the next scale.

• Step 4: Repeat step 3 until as many scales as desired


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original

L H

LH HH

HLLL

LH HH

HL

One scale two scales

��DecompositionDecomposition


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Figure: 2D Decomposition Wavelet Analysis

Figure: Decomposition levels of Subsignal


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Figure: 2-D DWT


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Figure: 2-D DWT Decomposition: a) Original image, b) One level decomposition, c)

Two levels decomposition, d) Three levels decomposition

ALGORITHMALGORITHM

�� DecompositioDecomposition

Step 1: Start-Load the source image data from a file into an array.

Step 2: Choose a Wavelet

Step 3: Decompose-choose a level N, compute the wavelet decomposition of

the signals at level N

Step 4: Compute the DWT of the data

Step 5: Read the 2-D decomposed image to a matrixStep 5: Read the 2-D decomposed image to a matrix

Step 6: Retrieve the low pass filter from the list based on the wavelet type

Step 7: Compute the high pass filter i=1

Step 8: i >= 1decomposed level, then if Yes goto step 10, otherwise if No goto

step 9

Step 9: Perform 2-D decomposition on the image i++ and goto to step 8

Step 10: Decomposed image


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Figure: 2-D IDWT

ALGORITHMALGORITHM

� Reconstruction

Step 1: Start-Load the source image data from a file into an array



the signals at level N

Step 4: Compute the DWT of the data

Step 5: Read the 2-D decomposed image to a matrixStep 5: Read the 2-D decomposed image to a matrix

Step 6: Retrieve the low pass filter from the list based on the wavelet type

Step 7: Compute the high pass filter i=decomp level

Step 8: i <= 1, then if Yes goto step 10, otherwise if No, goto step 9

Step 9: Perform 2-D reconstruction on the image and goto step 8

Step 10: Reconstruction image


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COMPRESSION TECHNIQUECOMPRESSION TECHNIQUE

• 1D: signal compression

• 2D: image compression

• Image Compression techniques classified into two categories:

– Lossy Compression

– Lossless Compression

• Reducing the amount of data required to represent a digital • Reducing the amount of data required to represent a digital image. Compression is achieved by the removal of one or more of three basic data redundancies.

– Redundancy reduction aims at removing duplication from the signal source (image/video).

– Irrelevancy reduction omits parts of the signal that will not be noticed by the signal receiver, namely the Human Visual System (HVS).


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Lossy image compression systemLossy image compression system

QuantizationThe lossy step


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Figure: Compression Technique

Lossless vs. Lossy CompressionLossless vs. Lossy Compression

Lossless Lossy

Reconstructed image numerically identical to

the original image

contains degradation

relative to the original

Compression rate 2:1 (at most 3:1) high compression

(visually lossless)

ALGORITHMALGORITHM

�� CompressionCompression




signals at level N

Step 4: Threshold detail coefficients, for each level from 1to N

Step 5: Remove(set to zero) all coefficients whose value is below a Step 5: Remove(set to zero) all coefficients whose value is below a

threshold(this is the compression step)

Step 6: Reconstruct, Compute wavelet reconstruction using the original

approximation coefficients of level N and the modified detail

coefficients of levels from 1 to N

Step 7: Compare the resulting reconstruction of the compressed image to the

original image.


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DENOISING TECHNIQUEDENOISING TECHNIQUE


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Figure: Denoising Technique

�For removing random noise

• DWT of the image is calculated

• Resultant coefficients are passed through threshold testing

• The coefficients < threshold are removed, others shrinked

• Resultant coefficients are used for image reconstruction

with IWT


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ALGORITHMALGORITHM�� DenoisingDenoising



Step 3: Decompose-choose a level N, compute the wavelet decomposition of the

signals at level N

Step 4: Add a random noise to the source image data

Step 5: Threshold detail coefficients, for each level from 1 to N,

Step 6: Reconstruct, Compute wavelet reconstruction using the original

approximation coefficients of level N and the modified detail coefficients

of levels from 1 to N

Step 7: Compare the resulting reconstruction of the denoised image to the

original image.


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EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS

•• Decomposition & ReconstructionDecomposition & Reconstruction

Image Used (grayscale)=kumar.jpg, Image size=147 X 81


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Figure: Original Image Figure: Reconstructed Image

Figure: 1st level Decomposition


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Figure: 2nd level Decomposition


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Figure: Decomposition approximations

At different Decomposition levelsAt different Decomposition levelsThreshold (thr) = 20, Image Used (grayscale)=kumar.jpg,

Image size=147 X 81

Table.1:

Coiflets

Wavelet

Compression

(Decomposition

Level)

Sl. No. Decom

positio

n levels

Short

Name

( w )

Compressed

Image

( % )

De-noising

Compressed

Image ( % )

Norm

Rec

Nul

Coeff

s

Norm

Rec

Nul

Coeffs

1 One coif4 99.91 73.70 100.00 46.86

2 Two coif4 99.90 85.52 100.00 46.86

3 Three coif4 99.93 86.66 100.00 46.86

4 Four coif4 99.97 84.68 100.00 46.86

5 Five coif4 99.99 82.31 100.00 46.86


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Figure: Coiflets

Wavelet

Compression

(Decomposition

Level)

5 Five coif4 99.99 82.31 100.00 46.86

6 Ten coif4 100.00 68.30 100.00 46.86

Coiflets Wavelet Compression(Threshold)Coiflets Wavelet Compression(Threshold)Level (n)= 5, Image Used (grayscale)=kumar1.jpg,

Image size=109 X 87, Wavelet Short name – ‘coif4’

Table.2 :

Coiflets

Compression

Wavelet

(Threshold)

Sl. No. Thresah

old (thr)

Compressed

Image

( % )

Denoising

Compressed

Image ( % )

Norm

Rec

Nul

Coeffs

Norm

Rec

Nul

Coeffs

1 10 99.99 82.61 99.95 81.57

2 20 99.97 89.35 99.95 81.57

3 30 99.94 92.07 99.95 81.57

4 40 99.92 93.73 99.95 81.57

5 50 99.89 94.64 99.95 81.57

6 60 99.86 95.45 99.95 81.57

7 100 99.71 97.12 99.95 81.57


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Figure:Coiflets

Wavelet

Compression(Thres

hold)

7 100 99.71 97.12 99.95 81.57

8 200 99.28 98.57 99.95 81.57

DeDe--noising noising

Image Used (grayscale)=kumar.jpg, Image size=147 X 81


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Figure. Coiflets Wavelet Denoising

CONCLUSIONCONCLUSION• All the wavelets having good denoised compression image

with clarity, but differ in energy retaining & percentage of

zeros.

• The denoising at lower level of decomposition having

reasonable clarity but at the higher levels the image is not

clear. clear.

• It is found that Coiflets wavelet for compression & denoising

at decomposition & thresholding is reasonably good.


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��Future WorkFuture Work

• To find the best thresholding strategy, wavelet for a

given image, to investigating other complex wavelet

families.

• Analyzing different image formats and experimenting

such as TIFF, GIF, BMP, PNG, and XWD. such as TIFF, GIF, BMP, PNG, and XWD.


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REFERENCESREFERENCES1. Stephen J. Chapman -“MATLAB Programming for Engineers”, page no. 1-74, 3rd

Edition 2005.

2. Rafael C. Gonzalez, Richard E. Woods, Steven L. Eddins – “Digital Image Processing Using MATLAB”, page no. 1-78, 256-295 & 296-547, 1st Edition 2006, www.mathsworks.com

3. Rudra Pratap - “Getting started with MATLAB7”, page no. 1-15, 17-44 & 49-79, 2nd

Edition 2006.

4. Rafael C. Gonzalez, Richard E. Woods – “Digital Image Processing”, page no. 15-17, 2nd Edition 2003,

5. Anil K. Jain – “Fundamentals of Digital Image Processing”, page no. 1-9, 15, 41, 135, 141, 145, 476, 2nd Indian reprint 2004.135, 141, 145, 476, 2nd Indian reprint 2004.

6. Maduri A. Joshi – “Digital image Processing and Algorithmic Approach”, page no. 1, 59-66, 2006, www.phindia.com

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8. Howard L.Resnikof, Raymond O. Wells – “Wavelets Analysis”, “the scalable structure of information”, page no.39, 191, 343, 2000 reprint, www.springer.de

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Indian reprint 2004.

10. Alan V. Oppenheim, Ronald W.Schafer – “Digital Signal Processing”, page no. 1, 87, 15th printing October 2000.


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11.John G. Proakis, Dimitris G. Manolakis - “Digital Signal Processing”, “Principles, Algorithms and Applications”, 3rd Edition December 2002

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18. Mallat.S. [1989a]. “ A Theory for Multiresolution Signal Decomposition: the Wavelet Representation, ”IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-II, pp.674-693.

19. Meyer.Y. (ed.) [1992a]. Wavelets and Applications: Proceedings of the International Conference, Marseille, France, Mason, Paris, and Springer-Verlag, Berlin.


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[20] Sonja Grgic, Mislav Grgic, Member, IEEE, and Branka Zovko-Cihlar, Member IEEE “Performance Analysis of Image Compression Using Wavelets” IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL. 48, NO. 3, JUNE 2001.

[21] Yogendra Kumar Jain & Sanjeev Jain -“Performance Analysis and Comparison of Wavelet Families Using for the image compression”. International Journal of soft Computing2 (1):161-171, 2007

[22] Wallace, The JPEG still picture compression standard, IEEE Trans. Consumer Electronics, 1992.

[23] Yong-Hwan Lee and Sang-Burm Rhee -” Wavelet-based Image Denoising with Optimal Filter” International Journal of Information Processing Systems Vol.1, No.1, 2005

[24] D.Gnanadurai, and V.Sadasivam -”An Efficient Adaptive Thresholding TechniqueforWavelet Based Image Denoising” International Journal of Information and Communication Engineering 2:2 2006.Engineering 2:2 2006.

[25] S.Arivazhagan, S.Deivalakshmi, K.Kannan –“ Performance Analysis of Image Denoising System for different levels of Wavelet decomposition” International Journal of Imaging Science And Engineering (IJISE), GA,USA,ISSN:1934-9955,VOL.1,NO.3, JULY 2007.

[26] Sachin D Ruikar & Dharmpal D Doye -“Wavelet Based Image Denoising Technique”(IJACSA) International Journal of Advanced Computer Science and Applications,Vol. 2, No.3, March 2011.

[27] Priyanka Singh Priti Singh & Rakesh Kumar Sharma -“JPEG Image Compression based on Biorthogonal, Coiflets and Daubechies Wavelet Families” International Journal of Computer Applications (0975 – 8887)Volume 13– No.1, January 2011.

[28] Krishna Kumar, Basant Kumar & Rachna Shah -“Analysis of Efficient Wavelet Based Volumetric Image Compression” International Journal of Image Processing (IJIP), Volume (6) : Issue (2) : 2012.


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[29] B.B.S.Kumar, Harish N.J, & Vinay.B - National Conference on Advance Communication Trends (ACT-2012) held on 23rd and 24th August 2012 at Bangalore, Organised by : Dept of ECE, Rajarajeswari College of Engineering. Paper title: Image Analysis using Haar Wavelet.

[30] B.B.S.Kumar & Rajshekar.T - National Conference on held on 27th and 28th March 2013 at Bangalore, Organised by : Dept of ECE, T. John Institute of Technology(TJIT). Paper title : Compression and Denoising analysis from still images using Discrete Meyer Wavelet Technique.

[31] B.B.S.Kumar, Harish N.J & Rajshekar.T - National Conference on Recent Trends in

Communication and Networking(NCRTCN-2013) held on 27th and 28th March 2013 at

Bangalore, Organised by : Dept. of Telecommunication Engineering, Don Bosco Institute of Technology(DBIT). Paper title: Compression and Denoising analysis from still images

using Daubechies wavelet Technique.

[32] B.B.S.Kumar & Harish N.J National Conference on Emerging trends in Electronics, Communication and Computational Intelligence(ETEC-2013) held on 20th to 22nd March 2013 at Bangalore, Organised by:Dept of ECE, Vivekananda Institute of Technology(VKIT), Bangalore. Paper title: Image Analysis using Biorthogonal Wavelet.

[33] B.B.S.Kumar & Dr.P.S.Satyanarayana International Conference on Recent Trends in Engineering & Technology (ICRTET-2013) held on 24th March 2013 at Bangalore, Organized By: IT Society of India, Bhubaneswar, Odisha, India. Paper title: compression and Denoising Comparative analysis from still images using Wavelet TechniquesISBN : 978-93-81693-88-18.


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Questions ?????


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Thank you!Thank you!Thank you!Thank you!


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