Image denoising using HUBNIHT

It is assumed here that you have downloaded the toolbox https://github.com/AmmarMian/huber_mm_framework and are now in the ./matlab folder

Contents

Set-up the path: it is assumed that you are in the ./examples folder

close all;
clc;
clearvars;
addpath('../');
addpath('../pics');
addpath('../aux');

Possible choices for Huber's threshold.

Due to very spiky salt and pepper noise, it is recommended to use a lower value for threshold for Huber's loss. A small value indicates increased robustness. In this example, we use c70 = 0.1917.

c95 = 1.345;
c85 = 0.7317;
c80 = 0.5294;
c75 = 0.3528783;
c70 = 0.1917;

load the Lena image and add noise

load lena256color.mat;
y0 = double(rgb2gray(X0));
clear X0;
y0 = y0/max(y0(:));  % making the pixel values lie in the interval [0,1]
n = 8; % use 8 by 8 windows

rng default;
y = imnoise(y0,'salt & pepper',0.1); % ADD SALT AND PEPPER NOISE
maxI = max(y(:));
N = size(y,1);

Plot the true and noisy images

figure(1); clf;
imagesc(y0);
colormap(gray(256));
axis image;
axis off;
title('Original Image');

figure(2); clf;
imagesc(y);
colormap(gray(256));
axis image;
axis off;

PSNRin = psnr(y,y0,maxI);
title(['Noisy Image with PSNR = ',num2str(PSNRin),' dB'],'FontSize',16);

Median filter denoising

youtMF = medfilt2(y,[3 3]);
tic;
PSNR_MF = psnr(youtMF,y0,maxI)
toc;
figure(3); clf;
imagesc(youtMF);
colormap(gray(256));
axis image;
axis off;
title(['Median Filter PSNR = ',num2str(PSNR_MF),' dB'],'FontSize',16);

PSNR_MF =

   26.2690

Elapsed time is 0.000655 seconds.

HUBNIHT denoising

Here we use K=11 as the value for sparsity level. For the chosen threshold value c, it gaved the best results. Note that hubniht_denoising function uses parallel pool to speed up the computation.

K = 11; % sparsity level to consider
c = c70; % threshold for Huber's loss function

horizontal = false; % denoise by both horizontal and vertical scan of patches

Setting up horizontal = false implies that scanning of patches is performed both in horizontal and vertical directions. The output is then average of the scans. For large images, it is recommended to set horizontal = true. This speeds up computations roughly by 1/2 as the vertical scan is not performed. This is illustrated at the end of this script.

tic;
[yout,yout_h,yout_v] = hubniht_denoising(y,n,[],c,K,[],horizontal) ;
toc;
PSNR(1) = psnr(yout,y0,maxI);
PSNR(2) = psnr(yout_h,y0,maxI); % horizontal
PSNR(3) = psnr(yout_v,y0,maxI);
PSNR

Elapsed time is 79.830923 seconds.

PSNR =

   28.8805   28.6378   28.7530

As can be noted, on my MacBook Pro laptop it took about 79 seconds to obtain the denoised image.

Plot the denoised image obtained by HUBNIHT

figure(4); clf;
imagesc(yout);
colormap(gray(256));
axis image;
axis off;
title(['HUBNIHT PSNR = ',num2str(PSNR(1)),' dB'],'FontSize',16);

HUBNIHT denoising: horizontal scan only

Note that the computation time using horizontal scan only is roughly 1/2 of the previous run.

horizontal = true; % denoise by horizontal scan of patches
tic;
[yout,yout_h,yout_v] = hubniht_denoising(y,n,[],c,K,[],horizontal) ;
toc;
psnr(yout,y0,maxI) % same as PSNR(2) computed earlier

Elapsed time is 43.309250 seconds.

ans =

   28.6378

Reference

Esa Ollila and Ammar Mian, "Block-wise minimization-majorization algorithm for Huber's criterion: sparse learning and applications", in Proc. IEEE International Workshop on Machine Learning for Signal Processing (MLSP), Sep 21-24, 2020, Espoo, Finland.

Published with MATLAB® R2019b