Speckle noise reduction

Speckle noise reduction: a review 

Advances in Seafloor-Mapping Sonar 

December 1st, Brest 

P. Courmontagne, Senior IEEE 

IM2NP / ISEN-Toulon, France

Speckle noise reduction: a review – Ph. Courmontagne 

2 

Synthetic Aperture Sonar 

‣ Achieve a good resolution 

‣ Drawback: the speckle noise 

Granular noise that inherently exists in SAS imagery 

By giving a variance to the intensity of each pixel, it reduces 

the spatial and radiometric resolutions 

Avoids thin interpretation and accurate details perception 

Speckle noise occupies a wider dynamic range than the scene 

content itself 

Reducing the speckle noise enhances radiometric resolution at 

the expense of spatial resolution 

Compromise speckle noise reduction / spatial resolution preservation


3 

Synthetic Aperture Sonar 

‣ Example of SAS data 

Data acquisition 

SHADOWS© [Jean, 2006] 

Sea bed (La Ciotat bay – France) 

Resolution: 15 cm 

2001 801 pixels 

250 

200 

150 

100 

50 

0 

SAS data


4 

Filter Assessment methods 

‣ Speckle Level – Variation Coefficient 

Obtained by computing the variation coefficient (C in the 

following) for several homogeneous areas of the data. 

Let W be the number of homogeneous areas H n , it comes 

This one is computed in the same areas before and after process 

and allows to compute the Speckle Level reduction 

The higher it gets, the better it is


5 

Filter Assessment methods 

‣ Ratio Image [Walessa, 2000; Achim, 2005] 

It corresponds to the ratio of the original image (speckled) by 

the de-noised image 

In areas of the image where the speckle is fully developed, this 

ratio should have the characteristics of pure speckle 

Any appearing edge or shape in the ratio image reveals a bad 

interpretation of the filter 

Several assessment methods are based on the ratio image 

Mean value (=1), equivalent number of look (SAR images); 

Variation coefficient, mean and speckle noise distributions

Speckle noise reduction: a review – Ph. Courmontagne 6 

‣ Mean filter 

Scalar Filters 

Each pixel value is replaced by the average value of its neighborhood in a 

M × M window 

The result quality is M-dependent 

‣ Median Filter [Pitas, 1990] 

Each pixel is replaced by the median of all pixels in the neighborhood in a 

M × M window 

D R D 

The result quality is M-dependent 

D R D 

‣ Hybrid Median Filter [Nieminen, 1986] 

Use a 2-way hybrid kernel 

 

Median values 

R R C R R 

D R D 

D R D 

Hybrid kernel, M=5


Scalar Filters: Mean Filter (M = 5) 

7 

250 

200 

Computing Time using 

a Mean Filter, M=3 

250 

200 

Computing Time T/T 0 1.2 

De-noised SAS data 

Variance Reduction 9.3 

Speckle Level Reduction 

4.9 

FOM 

0.62 

150 

150 

Ratio Image 

Variation Coefficient Distribution 

100 

100 

Standard Deviation 

0.95 

0.046 

Mean Distribution 

50 

50 

1 


0.038 


0 

Ratio Image 

0 

Speckle Noise Distribution 

Correlation Factor 

108


8 

Adaptive Filters 

‣ Perform digital signal processing and adapt their 

performance based on the input signal 

‣ Adaptive filters appear under two forms: 

Summation of a weighted noisy data and the mean through the 

processed window 

performed using a sliding sub-window processing ( p,q and 

E{Z p,q } are computed for each window) 

Averaging on a part of the pixel values present in the processed 

window by the use of masks


9 

‣ Henri’s filter 

Adaptive Filters – 1 st form 

Based on the local estimation of the data and noise variances 

‣ Lee’s filter [Lee, 1981; Lee, 1986] 

Signal estimation by mean square error minimization 

mean filter in homogeneous area, noisy data in edge area 

‣ Modified Lee filter [Lu, 1996] 

Performs a speckle noise reduction in edge area 

‣ Enhanced Lee filter [Lopes, 1990] 

The SAS image is divided in 3 classes: homogeneous (mean filter), 

heterogeneous (Lee’s filter) and strong heterogeneity (pixel value is 

preserved)


10 

‣ Kuan filter [Kuan, 1987] 

Adaptive Filters – 1 st form 

Multiplicative noise model transforms into a signal-dependent additive noise 

model + Minimum mean square error criterion 

‣ Modified Kuan filter [Lu, 1996] 

The Kuan filter derives from a linear approximation (1 st order Taylor 

expansion) Modified Kuan: the approximation is extended to 2 nd order 

Taylor expansion 

‣ Adaptive Frost filter [Frost, 1982] 

Equals to Wiener filter adapted to speckle model 

‣ Enhanced Frost filter [Lopes, 1990] 

Same approach as for the enhanced Lee filter


Adaptive Filters – 1 st form: Enhanced Lee Filter 

11 

‣ Results (M = 7) 

250 

200 

250 

200 





5.9 

FOM 

0.57 

150 

150 

Ratio Image 


100 

100 


0.92 

0.057 


50 

50 

1 


0.040 


0 

Ratio Image 

0 



66


12 

Adaptive Filters – 2 nd form 

‣ Adaptive mean filter [Pomalaza-Raez, 1984] 

Removes from the filtering window the pixels that have a too atypical value 

‣ Anisotropic diffusion filter [Perona, 1990] 

Diffusion process: the diffusion is isotropic in homogeneous regions and 

becomes anisotropic when a gradient is encountered. 

‣ Adaptive weighted d filter [Issa, 1996] 

It aims to smooth the noise and simultaneously enhance edges and preserve 

thin structures 

‣ Autoadaptive mean filter [Courmontagne, 2007] 

Based on the Mean Filter using for each pixel the most adequate window 

size, conditioned by the estimated signal first order statistics 

‣ Non-local mean filter [Buades, 2005] 

Based on the fact that images contain an extensive amount of self-similarities


Adaptive Filters – 2 nd form: Autoadaptive mean filter 

13 

‣ Results (circular window, M max = 27) 

Computing Time T/T 0 20 

250 

200 

250 

200 


Variance Reduction 14 


12 

FOM 

0.04 

150 

150 

Ratio Image 


100 

100 


1.07 

0.074 


50 

50 

1.03 


0.060 


0 

Ratio Image 

0 



149


14 

‣ Principle: 

Adaptive Filters in Transform Domain 

The idea is to apply different signal decompositions to the SAS 

data just followed by a process adapted to the new domain 

Two main families of expansion 

Discrete Wavelet Transform (Multi-resolution analysis) 

Signal expansion in a weighted sum of uncorrelated 

random variables, where the basis depends on a priori 

knowledge of signal and noise statistics


15 

Adaptive Filters in Transform Domain 

‣ Wavelet expansion & soft or hard thresholding 

The SAS data is expanded into several complementary sub-spaces (Mallat 

[Mallat, 1989], à Trous [Holdschneider, 1989]) 

Only a few part of the wavelet coefficients are kept (soft and hard 

thresholding [Donoho, 1993]) 

Only available for a Gaussian disturbing signal Ridgelet [Candes, 1998], 

Curvelet [Starck, 2002] and Gaussianisation [Mallet, 2000] 

‣ Stochastic Matched Filter (SMF, [Cavassilas, 1991]) 

SAS data expansion onto a basis enhancing the SNR; signal approximation 

reconstruction using only a few part of the decomposition coefficients 

Mean square error minimization [Chaillan1, 2005], speckle noise local 

statistics [Courmontagne, 2007], adaptive [Courmontagne, 2006] 

Coupled with multi-resolution analysis: à Trous algorithm [Chaillan, 2006], 

Mallat algorithm [Chaillan2, 2005]


Adaptive Filters in Transform Domain: ASMF 

16 

‣ Results (M max = 27, M min = 3) 

Computing Time T/T 0 13 

250 

200 

250 

200 


Variance Reduction 17 


15 

FOM 

0.05 

150 

150 

Ratio Image 


100 

100 


0.93 

0.062 


50 

50 

1 


0.063 


0 

Ratio Image 

0 



58


17 

Maximum A Posteriori (MAP) Filters 

‣ Using Bayesian approach, those filters intend to maximize the a 

posteriori probability P(S/Z) 

‣ Filters’ equations are derived by solving the MAP equation 

Assume a non-stationary multiplicative speckle noise model 

Too small windows introduce a bias 

‣ Several approaches depending on the distributions used to 

described the signal and P(Z/S) 

Kuan MAP filter [Kuan, 1987] 

Gamma MAP filter [Lopes, 1993] 

Fisher MAP filter [Nicolas, 2003]


MAP Filters: Gamma MAP Filter 

18 

‣ Results (M = 9) 

250 

200 

250 

200 





9 

FOM 

0.49 

150 

150 

Ratio Image 


100 

100 


0.95 

0.036 


50 

50 

1 


0.043 


0 

Ratio Image 

0 



144


19 

Conclusion 

‣ What is the best de-noising process ? 

Quite difficult question 

Depends on the use of the despeckled SAS data (detection, 

classification, …) 

Adaptive filters seem to be a good compromise 

‣ Other approaches 

Based on the use of filtering process directly on the received 

signals before beamforming 

Based on a mixing of known de-noising process


20 

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