XDU

XIDIAN

UNIVERSITY

SAR Image Despeckling Based on ImprovedDirectionlet Domain Gaussian Mixture Model

Biao HouKey Laboratory of Intelligent Perception and Image y y g p gUnderstanding of Ministry of Education of China

Xidian University, Xi'an, P. R. ChinaInstitute of Intelligent Information Processing (IIIP) 1

Xidian University, Xi an, P. R. China

ContentsContents

The main contents consist of the following parts:

Introduction 1

Cartoon-Texture Decomposition 2

Despeckling procedure 3

Results 4

2

IntroductionIntroduction

Speckle reduction is an important issue in SAR imageSpeckle reduction is an important issue in SAR image processing.Typical methods:

Spatial domain: Lee filter, Gamma MAP filter etc al; Transform domain: wavelet, many multiscale geometric

analysis based techniquesanalysis-based techniques.

In 2005, V. Velisavljevic et al. proposed Directionlet, which represents an image sparsely while capturing anisotropicrepresents an image sparsely while capturing anisotropic structures.

We improve the Directionlet transform to represent SARWe improve the Directionlet transform to represent SAR images much more sparsely and efficiently.

3Vladan Velisavljevic, Baltasar Beferull-Lozano, Martin Vetterli. Directionlets: Anisotropic Multidirectional Representation with Separable Filtering. IEEE trans. Image Processing. 2006,7,15(7),1916-1933.

In this topic we will address an efficient SAR imageIn this topic, we will address an efficient SAR image despeckling method based on:

N l ddi i d lNon-log additive model;

Cartoon texture decomposition;

The improved Directionlet transform;

Gaussian Mixture ModelGaussian Mixture Model.

4

Speckle noise modelSpeckle noise model

speckle noise is a natural consequence of image formationspeckle noise is a natural consequence of image formation under coherent radiation, which is generally modeled as multiplicative random noise, i.e.p ,

Log-transform is usually employed to make theX YF=

Log transform is usually employed to make the multiplicative speckle noise additive. Multiplicative speckle noise can also be converted into additive noise without the use of the log-transform:

( 1)X YF Y Y F= = + −

5

Cartoon texture decompositionpThe model is derived from the ROF model with total

variation minimization combining with the space of oscillatingvariation minimization combining with the space of oscillating functions.

In the ROF model a SAR image is represented as:2 2( )f L R∈

is the cartoon partis the cartoon part Is the texture partIs the texture part

In the ROF model, a SAR image is represented as:( )f L R∈( , ) ( , ) ( , )f x y u x y v x y= +

u vis the cartoon partis the cartoon part Is the texture partIs the texture part

piecewise regions

u v

remaining texturepiecewise regions

shape edges

remaining texture

noise

should be retained need to be processed

6Rudin, L., Osher, S., and Fatemi, E. (1992). Nonlinear total variation based

noise removal algorithms. Physica D 60, 259–268.

ExampleExample

SAR Field imagethe noise is mainly

contained in the texture part

Cartoon texture d itidecomposition

The cartoon part The texture part

7An example of the cartoon texture decomposition.

Directionlet

Directionlet is an extension of wavelet transform to manyDirectionlet is an extension of wavelet transform to many directions.

Using Directionlet transform, an image can be partitioned into several independent cosets, where the skewed anisotropic wavelet transform (AWT) is performed in different directionswavelet transform (AWT) is performed in different directions.

Directionlets trace the discontinuity efficiently with fewer significant coefficients so it can represent highly anisotropicsignificant coefficients, so it can represent highly anisotropic objects like contours and edges more precisely.

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The improved DirectionletThe improved Directionlet

Performing the skewed-AWT directly to the cosets obtained by the first decomposition and fitting model result in over-sharp a peak at zero point so that the curve can not be fittedsharp a peak at zero point, so that the curve can not be fitted correctly.

W i th t d iti i 2 l lWe improve the coset decomposition, proposing a 2-level coset decomposition, that is, coset decomposition is performed once more on the cosets obtained by the firstperformed once more on the cosets obtained by the first decomposition.

The 2 level coset decomposition is reversibleThe 2-level coset decomposition is reversible.

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The improved DirectionletThe improved Directionlet

10

GMM representationsGMM representations

A i th t i th i Di ti l t ffi i t itAssuming that is the noisy Directionlet coefficients, its mixture probability density function is given by

XW

∑ X0,1

( ) ( ) ( )XW X

kp W p S k p W S k

=

= = =∑( ) 1p S k= =∑

0,1

( ) 1k

p S k=∑

21( ) exp( )2Xxp W S kd

= = −

where is a mixture parameter, and is

( ) p( )22X

kk

pddπ

( )p S k= ( | )Xp W S k=

the probability density function of the k-th Gaussian component, with mean 1 and variance .kd

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co po e t, w t ea a d va a ce .kd

GMM fittingGMM fitting

Fitting results

The solid lines with violent oscillation denote coefficient curves of the high-frequency sub-bands in the cosets, and the smoothing solid lines are the results of fitting.

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the results of fitting.

GMM-based estimate of noiseGMM based estimate of noise

For the high-frequency coefficients ，Bayes estimate( )W i jFor the high-frequency coefficients ，Bayes estimate of the noise-free Directionlet coefficients is given by

( , )YW i j

YW

ˆ

Based on a GMM of the PDF，the MMSE estimate of

Y XW Wη=

noise-free Directionlet coefficients is2 2

ˆ W Wσ σ−∑ 2

0,1( ) x B

x

W WY X X

k W

W p S k W Wσ=

= =∑

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A di t th B i l hAccording to the Bayesian rule, we have( | ) ( )( | ) .

( )X

Xp W S k p S kp S k W

W= =

= =

The noise standard deviation is estimated with a heuristic i i

( | )( )X

X

pp W

priori:

( ( )) / 0.6745BW X Xmedian W median Wσ = −

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FlowchartFlowchartInput SAR image

Cartoon texture decompositionProcessing

Cartoon part Texture part

Keep it the I d Di ti l t t feep t t esame Improved Directionlet transform

Estimate high-frequency coefficients by GMM

MMSE denoising

Inverse transform

t t

+

15

output

ResultsResults

（a） （b） （c）(a) original

（a） （b） （c）(b) G-MAP

(c) WT

(d) SWT

(e) NSCT

C i f d i i l f h SAR fi ld（d） （e） （f）

(f) Proposed

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Comparison of denoising results of the SAR field image.

DetailsDetails

（a） （c）（b）(a) first detail

（a） （c）（b）(b) NSCT

(c) Proposed

(d) second detail

(e) NSCT

（e）（d） （f）

(f) Proposed

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The details of the denoising results.

Performance comparisonPerformance comparison

ENLMean Std

Mean Ratio (%)Region1 Region2 Region3 ( )

Original 3.12 2.94 2.67 106.87 53.73 1.0000

G MAP 15 95 10 64 113 55 106 26 42 45 0 9943G-MAP 15.95 10.64 113.55 106.26 42.45 0.9943

WT 21.90 14.33 12.73 96.93 36.07 0.9070

SWT 55.95 27.42 60.41 89.97 28.43 0.8419

NSCT 48 56 26 52 30 23 99 81 33 27 0 9339NSCT 48.56 26.52 30.23 99.81 33.27 0.9339

proposed 55.72 68.53 175.06 106.75 21.43 0.9989

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d

ConclusionConclusion

We address a novel speckle reduction method combiningWe address a novel speckle reduction method, combining the cartoon-texture model with the GMM in the improved Directionlet domain.

The results demonstrates that the method achieves effective despeckling performance in:effective despeckling performance in:

subjective visual quality

details preservation

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Thank You!Thank You!

Institute of Intelligent Information Processing (IIIP) 20