Anisotropic Diffusion for Speckle Reduction of SAR Image Meihua Xie xmhdjh@163.com Department of mathematic and system science Science college, National university of defense technology

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

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

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.

I. Anisotropic diffusion for image denoising

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

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

Our anisotropic diffusion for image denoising Construction of eigenvector

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

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

The property of new diffusion tensor

The property of new diffusion tensor

Numerical results

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

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

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

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

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.

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

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.

III.Speckle reduction of SAR image Results

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 79.9887 186.77 Ex6 1.853 6.7244 23.1568 9.439 17.6513 121.35

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.

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

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

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.

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

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

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

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.

IV Fast algorithm based on CMG-PDE Original PDE Algorithm Results Image Original PDE Algorithm CMG-PDE Lenna PSNR (dB) Time (s) 30.8580 209.3750 30.7311 157.4380 37.0323 1148.5 37.5251 669.6720 Cameraman 34.5420 199.4370 34.7009 121.7500 38.2991 1.1697e+003 39.2838 724.160 Bacteria 33.2711 79.9530 33.2735 50.5000 37.2298 235.2500 39.1966 152.5320

Thank You！