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CHAPTER 5

FILTERING ALGORITHMS FOR REMOVAL OF MULTIPLICATIVE SPECKLE NOISE IN

IMAGES WITH EDGE PRESERVATION

5.1 INTRODUCTION

Synthetic Aperture Radar (SAR) is an active sensor that uses

microwave signals for transmission and it detects the wave that is reflected

back by the objects. SAR is widely used for obtaining high resolution images

of the earth. It is used in the fields of remote sensing, oceanography, geology,

ecology and interferometry. Pixels in the image represent the back scattered

radiation from an area in the imaged scene. Brighter areas are produced by

stronger radar responses and darker areas are from weaker radar responses.

Speckle noise is an undesirable effect caused by coherent

reconstruction of the image and gives the image a grainy appearance. Speckle

may be modelled as a correlated signal and it is modelled as a multiplicative

noise in contrast to additive Gaussian and impulse noise as explained by

Zaman and Moloney (1993). Speckle noise is the primary source of

corruption in coherently illuminated images. Typical noise smoothing

methods are not well suited for the removal of speckle noise as explained by

Mark and Qing (1995). Various researchers, namely, Lee, Kuan, Frost have

proposed speckle removing algorithms useful for the radar community. The

filter algorithm proposed by Lee (1981) is based on the variance over an area

and smoothing will be performed only if the variance is low or constant over

an area. Another disadvantage is that the speckle noise in the edges is not

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removed by the filter. A simple speckle smoothing algorithm proposed by Lee

(1983) is based on the sigma probability of a Gamma distribution and is

effective in removing speckle but does not perform well in preserving edges.

This is because of the fact that if edges do not lie in the two sigma range, they

are not considered for averaging. The two sigma filter removes noise and the

smoothed image suffers some contrast loss as stated by Lee (1983). The kuan

et al (1987) filter is considered to be superior to the Lee filter. It simply

models the multiplicative noise of speckle into an additive linear form, but it

relies on the ENL from a SAR image. The only limitation with kuan filter is

that the ENL parameter is needed for computation. The Enhanced Frost filter

proposed by Lopes et al (1990) is an extension of the Frost filter that further

divides the image into homogeneous, heterogeneous and isolated point target

areas. By using this filter, the speckle noise in the heterogenous regions is

reduced but not removed so as to preserve the quality of image. De noising

using wavelet based algorithm is also known to be more efficient than

standard speckle filters. But they have a disadvantage of more computational

complexity than the speckle removing filters based on local order statistics

and also they require a compact support of wavelet basis functions that allows

wavelet transformation to efficiently represent the signals which have

localised features.

The adaptive filters that have been proposed in the earlier chapters

are tested with the images contaminated by speckle noise. Even though

adaptive filters perform well for any kind of image and any kind of noise, it is

found that the filters proposed in the chapters 2, 3, 4 do not completely

remove speckle noise. In order to remove speckle noise completely with edge

preservation properties, a computationally efficient and simple algorithm is

proposed in this chapter. The subjective and objective analyses of the filters

are done and the filter is compared with the standard sigma filter, mean,

median and adaptive bidirectional max/median filters.

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5.2 SPECKLE SMOOTHING ALGORITHM WITH EDGE

PRESERVATION

5.2.1 Noisy corrupted image model

The original signal is corrupted by a multiplicative noise of mean 1

and variance σn. It is given as below

),(),(),( jinjixjis (5.1)

where x(i,j) is the original signal , n(i,j) is the multiplicative noise whose

statistics depend on the signal and s(i,j) is the noise corrupted signal.

5.2.2 Proposed filter Algorithm

A new filtering structure is proposed to remove speckle noise with

edge preservation and removal of noise in the edges also.

The proposed algorithm is based on local order statistics to remove

speckle noise with edge preservation capabilities and the filtering algorithm is

given the name ‘New Filter III’.

The block diagram of the proposed filter is depicted as below

Figure 5.1 Block diagram of New Filter III

3 sigma filter

Edge detector

Reconstructed image y(i,j)

Corrupted image,s(i,j)

f(i,j)

e(i,j)

Filtering of Edges (If they are corrupted)

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The algorithm is explained as below.

The corrupted signal pixels are designated as s(i,j). The mean of s(i,j) is

),(),(),(),( jixjinjixjis (5.2)

This is because of the established fact in theory that speckle obeys a negative

exponential distribution and, therefore, is multiplicative in nature in the sense

that its standard deviation is equal to its mean.

5.2.2.1. 3 Sigma filter

The corrupted image is processed by a 3 sigma filter as below

i) Let the corrupted signal considered within m x n window be

s(m,n)and its variance is calculated as

Var(s(m,n)) = [standard deviation of s(m,n)/mean of s(m,n)]2; (5.3)

ii) Let the average value of the pixels of ‘s’ be mean(s(m,n)) and

the lower and upper intensity values are calculated as

)),(var()),((3),(( nmsnmsmeannmsmeancl (5.4)

)),(var()),((3),(( nmsnmsmeannmsmeancu (5.5)

iii) The intensity value of each pixel inside the window is compared

with the values of cl and cu. If it lies between the limits of cl

and cu, then the pixel is considered to be the pixel within the

lower and upper variance limits. The centre pixel in the window

is then replaced by the mean of the pixels whose intensity

values lie between cl and cu.

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Since the intensity values lying within the limited variance are

involved in the averaging, the speckle noise is removed with better reduction

in blur.

Since the noise is multiplicative, the intensity value of the corrupted

pixels is high if the value of the original brightness of the pixel is very high.

In 3 sigma filter, the pixels within the prescribed standard deviation are

averaged. Since the edges are of high intensity values, they are not involved

in the averaging process. In order to preserve these discarded edges, a high

pass filter is used to detect edges and the edges are preserved. The edges are

preserved if they are not corrupted and they are replaced by the non corrupted

neighbourhood pixel in case of corruption.

5.2.2.2 Edge detection and preservation

The edges in an image are detected using a computationally simple

technique ie., using a high pass filter. Edges are of high intensity values and if

they are corrupted by multiplicative noise, their intensity values are further

increased. The edges can be identified by comparing the absolute value of the

difference in the amplitude of the two samples with a threshold. For an image

of s(i,j) with a window 3×3, the edges in all the four directions such as the

horizontal, vertical, diagonal and sub diagonal directions are detected as

eh(i,j), ev(i,j),ed(i,j) and esd(i,j) .e(i,j) is considered as eh(i,j), the horizontal

edge if

| e(i-1,j) –e(i,j) | > ‘t’ (or) | e(i+1,j) –e(i,j) | > ‘t’

e(i,j) is considered as ev(i,j) , the vertical edge if

| e(i,j-1) –e(i,j) | > ‘t’ (or) | e(i,j+1) –e(i,j) | > ‘t’

e(i,j) is considered as ed(i,j) , the diagonal edge if

| e(i-1,j-1) –e(i,j) | > ‘t’ (or) | e(i+1,j+1) –e(i,j) | > ‘t’

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e(i,j) is considered as esd(i,j) , the sub diagonal edge if

| e(i-1,j+1) –e(i,j) | > ‘t’ (or) | e(i+1,j-1) –e(i,j) | > ‘t’

The optimum value of ‘t’ is found by using many images and different

amounts of noise.

In theory, the objective quality of the image is not degraded if a

pixel is replaced by the neighbourhood pixel. This is because of the fact that

the pixel along with its neighbourhood pixels influences the visual

interception. Hence if the edges are found to be corrupted by speckle noise,

they are replaced by the minimum neighbourhood uncorrupted pixel. The

signal is identified as corrupted by multiplicative noise by the fact that the

‘coefficient of variation’, (ratio of the standard deviation to the signal value)

remains constant. Hence the output of the edge filtering block is free from

noise and thus the edges are preserved and are free from noise.

The reconstruction block does the work of combining the output of

the 3 sigma filter and the output of the edge filter. If e(i,j) = 0, then the

output= f(i,j) and if f(i,j)=0, then output=e(i,j). Thus the simple technique

efficiently provides the output image which is free from speckle noise. The

edges are preserved and noises in edges are also removed.

5.3 RESULTS AND DISCUSSION

The proposed algorithm is tested using a remotely sensed image of

256 × 255 pixels with 8 bits /pixel and a natural image ‘Lena’ image of

256 × 256 pixels with 8 bits /pixel. The original image is corrupted with a

speckle noise at different densities.

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The performance of the filter is evaluated both quantitatively and

qualitatively. The evaluation measures used to evaluate the performance of

the filter are Mean Square error/pixel, Image Enhancement Factor, Peak

Signal to Noise Ratio, Noise Variance and Equivalent Number of looks

(ENL).

The definitions of MSE/pixel, IEF, PSNR are presented in

chapter 2. Guo et al (1994) proposed two approaches of estimating the

speckle noise level. They are

i) Measuring ENL over a uniform image region

ii) Noise variance.

A lower MSE indicates a less difference between the original image and

filtered image. This means that there is a significant noise reduction. A higher

value of IEF denotes not only the higher noise reduction and also the greater

enhanced image. Higher the value of PSNR refers to the better performance

of filter in eliminating the noise.

5.3.1 Equivalent Number of Looks (ENL)

A larger value of ENL corresponds to a better quantitative

performance. The value of ENL also depends on the size of the tested image.

In this work ENL is calculated for 4 noise looks. The formula for ENL

calculation is given by

2

ENL (5.6)

where µ is the mean of the uniform region and σ is the standard deviation of

the uniform region.

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5.3.2 Noise variance (NV)

NV determines the contents of the speckle in the image. A lower

variance gives a smoother image as more amount of speckle is reduced. The

formula for calculating the noise variance is given as

1

0

1

0

22 ),(1 N

i

N

jjiu

N (5.7)

where u(i,j) is the de noised image at (i,j)th spatial coordinate.

The noisy image is formed by multiplying speckle of various

densities. This noisy image is processed by the proposed filter with a window

size of 3×3 and 5×5.

The performance of the filter is compared with the median, simple

speckle smoothing algorithm by Lee, Frost filter, Kuan filter, MATMF in

terms of MSE, IEF, PSNR, NV, ENL and is shown in Table 5.1. A remotely

sensed image is corrupted by a speckle of density 0.05 and processed by a

window of size 5×5. The higher value of PSNR, IEF and ENL for the

proposed filter shows the better performance comparatively. Lower value of

MSE/ pixel and NV is also a factor of its improved performance. The value of

MSE/pixel increases with the increase in the amount of noise.

The qualitative analysis of the performance of the filter is shown in

Figure 5.2. In this analysis, the original remotely sensed image is corrupted by

a speckle noise of variance 0.02, 0.05 and 0.1 and the results of the algorithm

for these corrupted images are depicted in Figure 5.2(a) through

Figure 5.2(g). The edge preservation and noise elimination is more if the

corrupted amount of noise is less.

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A comparative analysis of the PSNR of various filters with that of

the proposed filter for various amounts of speckle noise is shown in

Figure 5.3. A higher value of PSNR shows an excellent performance of the

proposed filter in terms of its noise elimination. The PSNR comparison has

been depicted using a remotely sensed image as the test image.

As depicted in Figure 5.4 the IEF shows the superior performance of

the new filter in terms of its noise elimination with the edge preservation

properties. The test image ‘Lena’ is corrupted by various amounts of speckle

noise. The performance is compared with the results of MATMF, median,

Lee, Frost and Kuan filters.

All the evaluation measures are calculated for a ‘lena’ image

corrupted by a speckle noise density of 0.1 and the comparative analysis is

shown in Table 5.2.

A graph in Figure 5.5 relating various noise densities and

MSE/pixel for the ‘lena’ image shows that the new filter offers lower

MSE/pixel than the MSE/pixel of other filters. It shows that more amount of

speckle noise is removed by the proposed filter.

If the ‘lena’ image is corrupted by a speckle noise intensity of 0.1

and they are processed by various filters. The qualitative performance of the

proposed filter is compared with the performance of the various adaptive

filters using Figure 5.6(a) to Figure 5.6(g). The proposed filter is found to

provide better edge preservation than the other filters.

A higher value of ENL is offered by the new filter in removing the

speckle noise in a remotely sensed image than the value of ENL while

removing the speckle noise in a lena image. This is depicted in Figure 5.7

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and it shows that the new filter performs well for the remote sensing image

than for a general image.

Even though many evaluation measures quantify the performance of

the New Filter III, as in the theory, the qualitative analysis is of more

importance for the human vision. The qualitative analysis of the filter is

compared with the results of other filters if the original remote sensing image

is corrupted with a speckle density of 0.1in Figure 5.8(a) through 5.8(g).

The mean of the remote sensing image is more than that of the lena

image. The performance of the filter using a remotely sensed corrupted image

is depicted in Table 5.3. The comparative performance of the New Filter III

on to the Lena image processed at different window size 3×3 and 5×5 is

shown in Table 5.4. As the window size increases, the values of PSNR

increases and the values of MSE/Pixel decrease for the proposed filter. This

shows that the noise reduction is more as the window size increases but the

quality of the images gets blurred.

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Table 5.1 Comparative analysis of the New Filter III in terms of various evaluation measures

(with remotely sensed image as test image)

Type of filter Speckle noise density

Evaluation Measures

MSE/pixel IEF PSNR ENL NV

General median filter 0.05 840 2.9 6.9 3.3 3.90E+04

MATMF 0.05 590 3.5 8.9 4.2 3.80E+04

Lee filter 0.05 342 3.3 11.7 3.8 3.80E+04

Enhanced Frost Filter 0.05 613 2.4 8.6 3.9 3.90E+04

Proposed filter 0.05 105 7.2 27.2 4.1 2.80E+04

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(a) (b) (c)

(d) (e) (f)

(g)

Figure 5.2 Qualitative illustration of the New Filter III (a) Original test

image. (b) ,(d) and (f) Original image corrupted with a

speckle noise of variance 0.1, 0.05 and 0.02 respectively (c),

(e) and(g) Results of the proposed filter for the noise

variance of 0.1, 0.05 and 0.02 respectively

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Figure 5.3 Comparison of quantitative performance of the

New Filter III in terms of PSNR with that of other filters

with the remotely sensed image as test image.

Figure 5.4 Comparison of quantitative performance of the New Filter

III in terms of IEF with that of other filters with the lena

image as test image

0

5

10

15

20

25

30

35

40

0.02 0.04 0.06 0.08 0.1Speckle Noise density

PSNR

Proposed f ilter

Enhanced Frost Filter

Median Filter

Lee Filter

MATMF

0

1

2

3

4

5

6

7

0.02 0.04 0.06 0.08 0.1

Speckle Noise variance

Imag

e En

hanc

emen

t Fac

tor

Proposed f ilter

Lee filter

Enhance Frost f ilter

Genealised median f ilter

M ATM F

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Table 5.2 Comparative analysis of the New Filter III in terms of various evaluation measures

(with lena image as test image)

Type of filter Speckle noise density Evaluation Measures

MSE/pixel IEF PSNR ENL NV

General median filter 0.05 203 3.7 11.4 2.4 3.20E+04

MATMF 0.05 193 4.4 16.6 2.9 3.15E+04

Lee filter 0.05 155 5.4 18.6 2.8 3.10E+04

Enhanced Frost Filter 0.05 356 3.3 12.3 2.6 3.16E+04

Proposed filter 0.05 130 6.7 21.1 3 3.00E+04

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Figure 5.5 Comparative analysis of the performance of the New Filter

III in terms of MSE/Pixel

0

50

100

150

200

250

300

350

400

450

500

550

0.02 0.04 0.06 0.08 0.1Speckle Noise density

MSE

/Pix

el

Proposed f ilter

Enhanced Frost Filter

Median Filter

Lee Filter

MATMF

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(a) (b) (c)

(d) (e) (f)

(g) Figure 5.6 Qualitative illustration of the New Filter III (using Lena

image as test image) (a) Original test image. (b) Original

image corrupted with a speckle noise density of 0.1(c) Result

of Enhanced Frost Filter (d) Image filtered by Generalised

median filer (e) Result of MATMF (f)Result of Lee filter

(g)Image filtered by New Filter III

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Figure 5.7 Comparative analysis of the performance of the New Filter

III in terms of ENL for a remotely sensed image and for

Lena image as test image

0

1

2

3

4

5

0.02 0.04 0.06 0.08 0.1Speckle Noise density

ENL

Remote sensing image

Lena image

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(a) (b) (c)

(d) (e) (f)

(g)

Figure 5.8 Qualitative illustration of the New Filter III (using remotely

sensed image as test image) (a) Original test image. (b)

Original image corrupted with a speckle noise density of

0.1(c) Result of Generalised median Filter (d) Image filtered

by Enhanced Frost (e) Result of MATMF (f)Result of Lee

filter (g) Image filtered by the proposed filter

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Table 5.3 Performance of the New Filter III for various window sizes with remote sensing image as test image

Type of filter

Evaluation Measures (remote sensing image corrupted by a speckle noise variance of 0.08)

Size of the window=3×3 Size of the window=5×5

MSE IEF PSNR ENL NV MSE IEF PSNR ENL NV

General median filter 931 2.9 6.3 3.1 3.90E+04 885 4.3 7.1 3.4 3.80E+04

MATMF 485 3.6 9.8 4 3.83E+04 373 0.5 3.6 3.66 2.68E+04

Lee filter 520 5.1 9.1 3.5 3.72E+04 490 3 8.9 4.5 3.70E+04

Enhanced Frost Filter 708 2.2 8.1 4 3.84E+04 928 0.7 7 3.65 3.86E+04

New Filter III 430 7.1 20 2.9 3.70E+04 362 5.1 14 3 3.60E+04

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Table 5.4 Performance of the New Filter III for various window sizes with lena as test image

Type of filter

Evaluation Measures ( Lena image corrupted by a speckle noise variance of 0.08)

Size of the window = 3×3 Size of the window = 5×5

MSE IEF PSNR ENL NV MSE IEF PSNR ENL NV

General median filter 516 3.2 8.2 2.5 3.14e+04 444 5.2 10 2.7 3.1e+04

MATMF 246 5.4 14.8 2.9 3.13e+04 230 5.7 4.9 2.8 2.15e+04

Lee filter 256 5.2 14.5 2.8 3e+04 270 4.9 14 2.8 3.05e+04

Enhanced Frost Filter 424 2.6 11.2 2.8 3.16e+04 587 2.6 9.6 3.05 3.1e+04

New Filter III 157 6.4 20 3.1 2.94e+04 143 5.1 23.2 3.2 2.87e+04

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5.4. CONCLUSION

The adaptive filtering algorithms proposed in chapters 2,3 and 4

work well for the simultaneous removal of additive mixture of Gaussian

noise and impulse noise. Though they are adaptive in nature, it has been

found that they do not perform well in removal of speckle noise. In order to

remove speckle noise which is multiplicative in nature and which

contaminates a remotely sensed image, a non linear adaptive filtering

algorithm has been proposed in this chapter.

The New Filter III is based on the local order statistics and the

qualitative results show that it removes speckle noise in a remote sensing

image with an excellent preservation of edges better than speckle noise

removal in general image. The test images are corrupted by various

intensities of speckle noise. The speckle noise is removed by a 3 sigma filter

which uses the local statistics such as mean and standard deviation of the

noise corrupted signal. The adaptive filter provides edge preservation by

using an edge detector which is a high pass filter and the replacement of the

corrupted edge by the neighbourhood uncorrupted signal. The reconstructed

filter algorithm combines the filtered signal from the 3 sigma filter and the

edges from the edge filtered signal to provide a noise free and edges

preserved image.

Various quantitative evaluation measures have been calculated to

prove the performance of the filter. The higher values of PSNR and lower

values of MSE/pixel show its superior performance in filtering the noise as

compared to other speckle removing adaptive filters. The qualitative analysis

of the filter shows the efficiency of the proposed filter in preserving the edges.

SAR images are corrupted by speckle noise and it has been proved that the

proposed algorithm works excellent for the remote sensing image than the

general images.