Simple example on Barbara

We present here the three variations of Gaussian Patch-PCA (GP-PCA) algorithms:

The first one is the global approach (using PGPCA.m) meaning all the patches in the images are used to compute a global PCA, followed by a hard-thresholding of the coefficients. The second one is the local approach (using PLPCA.m) meaning that we use a sliding window on which the PCA is performed, before hard- thresholding coefficients. The third one is the hierarchical or tree based approach (using PHPCA.m). We keep axis at some iteration and then look for axis on the complement of the space the span of the axis already found.

Authors: \( \textbf{C-A. Deledalle} \), \(\textbf{J. Salmon} \) and \(\textbf{A. S. Dalalyan} \)

Initialization

clear all
close all

sigma=10;
randn('seed', 2);
ima = double(imread('data/barbara.png'));
ima_nse = ima + sigma * randn(size(ima));

figure('Position',[100 100  800 800]);
plotimage(ima_nse);
title(sprintf('Noisy: \n  PSNR %.2f', psnr(ima, ima_nse)));
set(get(gca,'Title'),'FontSize',12);

GLOBAL VERSION: PGPCA.m

[hP factor_thr] = PGPCA_best_params(sigma);
threshold = factor_thr * sigma;
func_thresholding = @(ima_ppca) ...
    hardthresholding(ima_ppca, threshold, sigma);
global_time=tic;

Patchization step

ima_patchs = spatial_patchization(ima_nse, hP);

Global PCA denoising step

[ima_patchs_fil ima_ppca_fil] = ...
    PGPCA_denoising(ima_patchs, func_thresholding);

Uniform reprojection step

ima_fil_PGPCA = reprojection_UWA(ima_patchs_fil);
global_time=toc(global_time);

Display

figure('Position',[100 100  800 800])
plotimage(ima_fil_PGPCA);
title(sprintf('PGPCA: \n  PSNR %.2f', psnr(ima, ima_fil_PGPCA)));
sprintf('PGPCA:\n PSNR: %.2f dB \n Computing Time: %.2f s.',...
    psnr(ima, ima_fil_PGPCA),global_time)
set(get(gca,'Title'),'FontSize',12);

ans =

PGPCA:
 PSNR: 33.63 dB 
 Computing Time: 7.84 s.

LOCAL VERSION: PLPCA.m

[hP factor_thr hW] = PLPCA_best_params(sigma);
threshold = factor_thr * sigma;
% Shift/Redudancy  parameter for the searching zone.
delta = hW; %< 2*hW+hP;
func_thresholding = @(ima_ppca) ...
    hardthresholding(ima_ppca, threshold, sigma);
local_time=tic;

Patchization step

ima_patchs = spatial_patchization(ima_nse, hP);

Local PCA denoising step

ima_patchs_fil = PLPCA_denoising(ima_patchs, func_thresholding, ...
                                 hW, delta);

Uniform reprojection step

ima_fil_PLPCA = reprojection_UWA(ima_patchs_fil);
local_time=toc(local_time);

Display

figure('Position',[100 100  800 800])
plotimage(ima_fil_PLPCA);
title(sprintf('PLPCA: \n  PSNR %.2f', psnr(ima, ima_fil_PLPCA)));
set(get(gca,'Title'),'FontSize',12);
sprintf('PLPCA:\n PSNR: %.2f dB \n Computing Time: %.2f s.', ...
    psnr(ima, ima_fil_PLPCA),local_time)

ans =

PLPCA:
 PSNR: 34.77 dB 
 Computing Time: 15.06 s.

HIERARCHICAL VERSION:PHPCA.m

[hP factor_thr depth nb_axis_kept] = PHPCA_best_params(sigma);
threshold = factor_thr * sigma;
func_thresholding = @(ima_ppca) ...
    hardthresholding(ima_ppca, threshold, sigma);
hierarchical_time=tic;

Patchization step

ima_patchs = spatial_patchization(ima_nse, hP);

Hierarchical PCA denoising step

[ima_patchs_fil ima_ppca_fil tree] = ...
    PHPCA_denoising(ima_patchs, func_thresholding, ...
                    depth, nb_axis_kept);

Uniform reprojection step

ima_fil_PHPCA = reprojection_UWA(ima_patchs_fil);
hierarchical_time=toc(hierarchical_time);

Display

figure('Position',[100 100  800 800])
plotimage(ima_fil_PHPCA);
title(sprintf('PHPCA: \n  PSNR %.2f', psnr(ima, ima_fil_PHPCA)));
set(get(gca,'Title'),'FontSize',12);
sprintf('PHPCA:\n PSNR: %.2f dB \n Computing Time: %.2f s.', ...
    psnr(ima, ima_fil_PHPCA),hierarchical_time)

ans =

PHPCA:
 PSNR: 34.55 dB 
 Computing Time: 12.25 s.

"Image denoising with patch based PCA: local versus global"
C.-A. Deledalle, J. Salmon, A. S. Dalalyan, BMVC 2011, PDF.

Corresponding Matlab toolbox ZIP.

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