1. Anisotropic Diffusion for Speckle Reduction of SAR Image
Meihua Xie
Department of mathematic and system science
Science college, National university of defense technology

2. Outline Anisotropic diffusion for image denoising Prior of SAR image
Speckle reduction of SAR image
Fast algorithm based on CMG-PDE

3. I. Anisotropic diffusion for image denoising
For denoising problem
Whose PDE is

4. I. Anisotropic diffusion for image denoising
The anisotropic diffusion equation can be written as
where D is a diffusion tensor
Eigenvalue
Eigenvector, corresponding to the edge direction and gradient direction respectively.

5. I. Anisotropic diffusion for image denoising

6. I. Anisotropic diffusion for image denoising
In traditional equation, eigenvalues are often written as
Eigenvector are often written as or

7. I. Anisotropic diffusion for image denoising
The direction of edge is not right

8. Our anisotropic diffusion for image denoising
Construction of eigenvector

9. New anisotropic diffusion for image denosing
Construction of eigenvaule
Edge direction
Gradient direction
Weight function
Smooth region
Edge region

10. New anisotropic diffusion for image denosing
Hence, we obtain the following anisotropic diffusion equation
Which can be solved by finite difference.

11. The property of new diffusion tensor

12. The property of new diffusion tensor

13. Numerical results

14. Numerical results (b) Anisotropic diffusion (d) Our method
(a) Blur image

15. II.Prior of SAR Image Prior of SAR image
Imaging Model of Synthetic Aperture Radar (SAR)
is speckle, which has a distribution with expectation of 1.
Gamma Distribution
Log-Gamma Distribution

16. II.Prior of SAR Image Prior of SAR image Distribution of magnitude
Distribution of gradient of magnitude
MSTAR Image

17. II.Prior of SAR Image Prior of SAR image (a) A MSTAR Image
Target region
Background region
Shade region
(a) A MSTAR Image
(b) The curve of sorted magnitude

18. III.Speckle reduction of SAR image
Speckle reduction model based on magnitude and gradient
Diffusion based on magnitude
Just use the information of magnitude will ignore the consistent of region, and led to false point. So we need to use gradient information still.

19. III.Speckle reduction of SAR image
Speckle reduction model based on magnitude and gradient

20. III.Speckle reduction of SAR image
Speckle reduction model based on magnitude and gradient
Note: We can also construct a diffusion coefficient
based on magnitude and gradient, but it is very difficult since there exists large difference between the distribution of magnitude and gradient.

21. III.Speckle reduction of SAR image
Results

22. III.Speckle reduction of SAR image
Speckle reduction model based on magnitude and gradient
Results of Effective Number of Looks (ENL)
Orignal
Lee
Frost
GammaMAP
SRAD
Our
method
Ex1
9.77
11.47
42.33
50.023
135.17
199.65
Ex2
27.89
92.06
164.66
171.92
324.25
381.54
Ex3
3.17
11.21
48.33
77.06
90.04
95.84
Ex4
25.576
78.526
127.17
172.73
223.07
Ex5
1.238
4.877
9.735
9.749
186.77
Ex6
1.853
6.7244
9.439
121.35

23. III.Speckle reduction of SAR image
Speckle reduction and target enhancement
The above method just reduces noise but does not enhance target, to enhance the target we should use the prior of SAR image furthermore.
The following regularization model is used to enhance the target usually, which uses the sparsity of SAR magnitude .
The above equation is a compressed estimation of , which often cause the loss of power in image and miss some edge.

24. III.Speckle reduction of SAR image
Speckle reduction and target enhancement
(a) Original MSTAR Image
(b) Image enhanced by regularization

25. III.Speckle reduction of SAR image
Speckle reduction and target enhancement
(a) Original Image
(b) Image enhanced by regularization

26. III.Speckle reduction of SAR image
Speckle reduction and target enhancement
To reduces noise and enhance target simultaneously, we construct the following variation model
Where
And the construction of the third item is similarly to the above speckle reduction model.
Note: is varied according to the points of image.

27. III.Speckle reduction of SAR image
Results
(b) Image enhanced by regularization
(c) Image enhanced by our method
(a) Original Image

28. III.Speckle reduction of SAR image
Results
(a) The 3dB main-lobe width
(b) The target clutter ratio

29. IV Fast algorithm based on CMG-PDE
For very large image, the solving of the above equation will be very slow. Here, we provide a method based on Cascadic Multigrid (CMG) and Partial Differential Equation (PDE)
What is Cascadic Multigrid (CMG)?
The main idea of CMG is similar to multigrid, which also solves the equation on coarse meshes and extrapolates the solution on coarse meshes to refined meshes;
But, in CMG, the solution on coarse meshes does not be revised by the solution on refined meshes, which is different to the method of multigrid

30. IV Fast algorithm based on CMG-PDE
The steps of the algorithm
Firstly, divide the image into several different scale levels, and denote the resolution of each level;
Secondly, solve the PDE equation on the coarse grid;
Thirdly, using a nonlinear extrapolation method extrapolates the results on coarse grid to finer grid;
Frothy, let the extrapolated results to be the initial value of PDE on coarser level and solve it.

31. IV Fast algorithm based on CMG-PDE Original PDE Algorithm
Results
Image
Original PDE Algorithm
CMG-PDE
Lenna
PSNR (dB)
Time (s)
1148.5
Cameraman
1.1697e+003
Bacteria

32. Thank You！