SAR Denoising Using Pre-trained CNN Models

Xiangli Yang1,3, Loıc Denis2, Florence Tupin1, Wen Yang3

1 Telecom ParisTech2 Universite de Saint-Etienne

3 Wuhan University

1st June 2018, Paris

Overview

SAR denoising with pre-trained models

I The models are trained for Gaussian noise using naturalimages

I The logarithm intensity of SAR data follows Fisher-Tippettdistribution.

Image with Gaussian noise SAR image with speckle

CNN for Image Denoising

Denoising CNN framework (DnCNN)

I Network Architecture : VGG networkthe size of convolutional filters 3*3, receptive field DnCNN35*35, and the corresponding depth is 17.

I Model Learning : residual learning

L(Θ) =1

2N

N∑i=1

‖R(yi ; Θ)− (yi − xi )‖2F (1)

The architecture of the DnCNN network

CNN for Image Denoising

Train DnCNN modelsFor Gaussian denoising with known noise level, DnCNN uses 400images of size 180*180 for training. The noisy image is generatedby adding Gaussian noise with a certain noise level from the rangeof Sigma = 10 : 5 : 75.

Y = X +Sigma

255N (0, 1) (2)

Y is the inputs of DnCNN, X is the ground truth.

ProblemHow to choose one suitable pre-trained model of 14 different noiselevel models ?

Two framework of SAR Denoising (1)

Homomorphic CNN

The framework of Homomorphic CNN

DnCNN models are not linear, so we adjust the range of Log-intensity. We try to approach the Fisher-Tippett distribution by anon-centered Gaussian distribution. Then, the pre-trained could bechosen by the variance and the normalization factor.

X = fΨ(1,L)(Y ) + (log(L)−Ψ(L))1n (3)

Two framework of SAR Denoising (2)

MuLog CNN

The framework of MuLoG CNN

The Fisher-Tippett distribution is considered. A MAP optimizationis used for solving problem :

X ∈ arg minx−logp(y |x)− λlogp(x) (4)

Two framework of SAR Denoising (2)

Plug-and-play ADMM

x (k+1) = arg minx∈Rn

f (x) +ρk2‖x −

(v (k) − u(k)

)‖2 (5)

v (k+1) = Dσk(x (k+1) + u(k)

)(6)

u(k+1) = u(k) +(x (k+1) − v (k+1)

)(7)

ρk+1 = γkρk , (8)

where Dσk is a denoising algorithm (in our case the homomorphic

CNN), and σkdef=√λ/ρk is a paramater controlling the strength of

the denoiser.

Experimental Results

Simulated SAR

(a) Simulated SAR (b) GT (c) BM3D

(d) MuLoG+BM3D (e) CNN (f) MuLoG+CNN

Experimental Results

Experimental Results

SAR image

(a) Saint Gervais (b) GT (c) BM3D

(d) MuLoG+BM3D (e) CNN (f) MuLoG+CNN

References

Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang

Beyond a Gaussian Denoiser : Residual Learning of Deep CNN for ImageDenoising

IEEE Transactions on Image Processing, 26(7), 3142 – 3155, 2017.

Charles-Alban Deledalle, Loıc Denis, Sonia Tabti, and Florence Tupin

MuLoG, or How to apply Gaussian denoisers to multi-channel SAR specklereduction ?

IEEE Transactions on Image Processing, 26(9), 4389 – 4403, 2017.

Stanley H. Chan, Xiran Wang, and Omar A. Elgendy

Plug-and-Play ADMM for Image Restoration : Fixed-Point Convergenceand Applications

IEEE Transactions on Computational Imaging, 3(1), 84 – 98, 2017.