PGPCA、PHPCA、PLPCA去噪代码解析
2024-05-09 09:57:13
一、整体Pipeline流程解析
clear all
close allsigma=10;
randn('seed', 2);
ima = double(imread('data/barbara.png'));
% 添加噪音
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
%
% 首先依据噪声大小来获取最佳参数:Patch的大小以及阈值因子
[WP factor_thr] = PGPCA_best_params(sigma);
% 最终设定的阈值 = 阈值因子 * 噪声参数sigma (可以理解为设定的阈值是以噪声sigma参数为基础的)
threshold = factor_thr * sigma;
% @(x)类似于Pythonz中的lambda匿名函数
% 此处函数的作用是将用PCA方法作用于含噪图片后的分解结构进行硬阈值处理
% 这里的func_thresholding单纯只是一个函数，还没有被调用
func_thresholding = @(ima_ppca) ...hardthresholding(ima_ppca, threshold, sigma);
% matlab使用tic和toc来统计程序运行时间
global_time=tic;
%% Patchization step
% 从含噪图片中提取大小为WP * WP的方形Patch块状结构
ima_patchs = spatial_patchization(ima_nse, WP);% 去噪的核心步骤:进行Patch的全局去噪，然后进行重建
%% 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
% 展示去噪效果，并计算PSNR
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);%% LOCAL VERSION: PLPCA.m
[WP factor_thr hW] = PLPCA_best_params(sigma);
threshold = factor_thr * sigma;
% Shift/Redudancy parameter for the searching zone.
delta = hW; %< 2*hW+WP;
func_thresholding = @(ima_ppca) ...hardthresholding(ima_ppca, threshold, sigma);
local_time=tic;
%% Patchization step
ima_patchs = spatial_patchization(ima_nse, WP);
%% 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)%% HIERARCHICAL VERSION:PHPCA.m
%
[WP 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, WP);
%% 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)二、各类子函数代码解析
1）根据噪音参数sigma来获取最佳参数，从这里的代码来看，最佳参数的获取完全是事先预定好的：当sigma=5,10,20时，对应的patch大小都为7, 而当sigma=40时，对应的patch大小直接变成12，这其实也就是在间接说明，越大的噪音需要越大的patch来进行处理；当sigma=5,10时设置的硬阈值因子都是2.5，当sigma=20,40的时候设置的硬阈值因子直接变成2.75，这说明越大的噪音需要越大的硬阈值来进行处理（因子越大 等价于 硬阈值越大) 。
function [hP factor_thr] = PGPCA_best_params(sigma)%PGPCA_best_params computes the parameters for PGPCA.m,
% optimized on a small data set.
% INPUT:
% sigma : standard deviation of the noise
% OUTPUT:
% hP : half size of the patch
% factor_thr : factor in front of the variance term for
% hardthresholding the coefficients
%
% [hP factor_thr] = PGPCA_best_params(sigma)
% Computes the best parameters hP and factor_thr for the using
% PGPCA_denoising.m for some values of noise level.
%
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)
%
%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)switch sigmacase 5hP = 7;factor_thr = 2.50;case 10hP = 7;factor_thr = 2.50;case 20hP = 7;factor_thr = 2.75;case 40hP = 12;factor_thr = 2.75;end
2）硬阈值处理：其实这里的sigma参数并没有用到，只是将ima_ppca.coefs中绝对值大于给定阈值的部分保留了，其余部分置0
function ima_ppca = hardthresholding(ima_ppca, threshold, sigma)%hardthresholding Hard thresholding the PCA coefficients
% INPUT:
% ima_ppca : structure of the noisy PCAs decompositions.
% threshold : threshold used for the hardthresholding
% sigma : standard deviation of the noise
% OUTPUT:
% ima_ppca : sturture of of the PCAs after hardthresholding
%
% ima_ppca = hardthresholding(ima_ppca, threshold, sigma)
% hard thresholding of the PCA coefficients from the ima_ppca
% structure.
%
%
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)% 这里的维度转化感觉很奇怪，
% 貌似是因为这里的阈值计算只能使用2维来计算
% 所以得先确保coefs是2维的
% 但是为了原样还原，所以必须得记录之前的维度信息coefs = ima_ppca.coefs;if size(coefs, 3) > 1 %如果coefs第三个维度的长度大于1，其实也就是在说coefs有三个维度isimage = 1;[M,N,P] = size(coefs);MN = M*N;coefs = reshape(coefs, MN, P);elseisimage = 0;[MN,P] = size(coefs);endcoefs = coefs .* (threshold < abs(coefs)); %保留coefs中绝对值大于阈值的部分if isimageima_ppca.coefs = reshape(coefs, M, N, P);elseima_ppca.coefs = reshape(coefs, MN, P);end
3）**空间PATCH块提取：这里无需进行任何形式的padding，只需要按照从左到右、从上到下的顺序滑动来获取每一个patch, 从左到右的每个patch是紧紧相互邻接的，也可以说stride=1,；从上到下的每个patch也是同样。因为没有设置padding，所以从原始图片中提取的总的patch数目是不等于原始图像的总像素数。这里返回了两个数据，一个是提取到的每一个patch数据, 即ima_patchs(size为【每列对应的patch数，每行对应的patch数，一个patch对应的像素总数WP * WP】)， 另一个是原始图像中的每个像素点出现在patch中的次数，也就是每个像素点对应多少个Patch).
function [ima_patchs, ima_normalization] = spatial_patchization(im_ini,WP)%spatial_patchization computes the collection of patches extracted from an image
%
% INPUT:
% im_ini : image of interest
% WP : width of the square patches to consider
%
% OUTPUT:
% ima_patchs : the collection of all the patches
% ima_normalization : number of patches to which each pixel belongs
%
% [ima_patchs, ima_normalization] = spatial_patchization(im_ini,WP)
% computes the whole collecitons of the patches of size WP x WP
% of an image im_ini. It also provides the number of patches to
% which each pixel belongs in the image.
%
%
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)[m,n] = size(im_ini);
ima_patchs=zeros(m-WP+1,n-WP+1,WP^2);
ima_normalization=zeros(m,n);for i=1:(m-WP+1)for j=1:(n-WP+1)xrange = mod((i:i+WP-1)-1,m)+1; % （m:n)包括m到n的所有整数，m和n都是闭区间yrange = mod((j:j+WP-1)-1,n)+1; B = im_ini(xrange, yrange);ima_patchs(i,j,:) = B(:);ima_normalization(xrange, yrange) = ...ima_normalization(xrange, yrange) + ones(WP,WP);end
end
4）PGPCA去噪核心部分：主要是做了三件事情，首先是对从图像上提取的所有patch进行PCA分解，得到PCA分解的结果，对应于 ima_ppca = ppca(ima_patchs)部分【1】；然后是对PCA分解的结果进行一个硬阈值来过滤掉噪音，对应于 ima_ppca_fil = func_thresholding(ima_ppca)部分【2】，返回的是一个去噪后的PCA分解结果；最后是对这个去噪后的PCA分解结果进行重建，重建得到的不是完整的这个图像，而是去噪图像理论上所有的patch块, 对应于代码ima_patchs_fil = reconstruction_ppca(ima_ppca_fil)【3】部分。在完成这些之后，在主程序会调用reprojection_UWA【4】部分从所有的patch块来还原出去噪后的完整图像，这个过程也就是从所有的patch块中来计算得到完整图像中每个像素点的值。
function [ima_patchs_fil ima_ppca_fil] = ...PGPCA_denoising(ima_patchs, func_thresholding)
%PGPCA_denoising computes the denoised patches, denoised image
% and tree structure using PLPCA (local PCAs)
%
% INPUT:
% ima_patchs : a collection of (noisy) patches
% func_thresholding : function that used to threshold the coefficients
% OUTPUT:
% ima_patchs_fil : structure of of the PCAs after func_thresholding
% reprojected in the space of patches
% ima_ppca_fil : structure of of the PCAs after func_thresholding
% but in the PCA domain
%
% [ima_patchs_fil ima_ppca_fil] = ...
% PGPCA_denoising(ima_patchs, func_thresholding)
%
%
%% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)ima_ppca = ppca(ima_patchs);ima_ppca_fil = func_thresholding(ima_ppca); % 还是结构体，只不过进行了噪音过滤ima_patchs_fil = reconstruction_ppca(ima_ppca_fil); %（506,506,49）
[1] 重点是将每个patch对应的49个像素点张成一维的向量，然后再进行PCA分解:
function patchs_ppca = ppca(patchs)%ppca computes the PCA of a collection of patches
%
% INPUT:
% patchs : a collection of (noisy) patches
% OUTPUT:
% patchs_ppca : structure of of the PCAs (coefficients +components)
%
%
%patchs_ppca = ppca(patchs) computes the pca structures in patch_ppca of the
% collection of patches from patchs.
%
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)
%
%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)if size(patchs, 3) > 1isimage = 1;[M,N,P] = size(patchs);MN = M*N;patchs = reshape(patchs, MN, P);elseisimage = 0;[MN,P] = size(patchs);end% 计算平均值，patchs 256036 * 49% cst_patchs 256036 * 1cst_patchs = mean(patchs,2);% pc_axis是pca的主成分或者说新坐标轴，(49, 49)% patchs_newbasis是新坐标轴上X的新坐标系数，(256036, 49)% varaxis是每个轴上的方差或者说特征值 (49,1)% patchs - cst_patchs * ones(1, P)就是对每一行的元素减去该行元素的均值% 而前面已经知道每一行元素实际对应于一个patch，所以这里实际上是对每个patch内的元素去均值化[pc_axis,patchs_newbasis,varaxis] = ...princomp_eig(patchs - cst_patchs * ones(1, P));% 【(256036, 1), (256036, 48)】patchs_ppca.coefs = [ cst_patchs*sqrt(P) patchs_newbasis(:,1:end-1) ];patchs_ppca.iddico = ones(MN,1); % （256036,1）%patchs_ppca.score_rpjct=ones(M,N);patchs_ppca.dicos{1}.size = P;% 【（49,1）（49,48）】patchs_ppca.dicos{1}.axis = [1/sqrt(P)*ones(P,1) pc_axis(:,1:end-1)];% （1,49)所有patch在49个像素点上各自的均值patchs_ppca.dicos{1}.mean = mean(patchs - cst_patchs * ones(1, P), 1);% 【0; (48， 1)】patchs_ppca.dicos{1}.varaxis = [0; varaxis(1:end-1)];if isimagepatchs_ppca.iddico = reshape(patchs_ppca.iddico, M, N); % （506， 506）patchs_ppca.coefs = reshape(patchs_ppca.coefs, M, N, P); % （506,506,49)end
[2] 对应于2）硬阈值部分
[3] 重点是每一部分patch重建的过程
function patchs = reconstruction_ppca(patchs_pca)%reconstruction computes the values of the patches, knowing the
% structure (dico+coefs) of the patch_pca
%
% INPUT:
% patchs_pca : structures of the patches in the PCA basis% OUTPUT:
% patchs : the patches in original domain
%
%patchs = reconstruction_ppca(patchs_pca)
% computes the patchs values knowing patchs_pca, the structure
% of those patches in the space spanned by dicos.
%
%see also reconstruction.m and prejection.m (inverse operation)
%
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)% 获取重建图像需要的参数，% 需要在新坐标轴上的坐标参数coefs、% 其他信息dicos(包括每个patch的像素数，每个patch去均值化后的均值，新的坐标轴、每个新坐标轴上的方差)if size(patchs_pca.coefs, 3) > 1isimage = 1;[M,N,P] = size(patchs_pca.coefs);MN = M*N;coefs = reshape(patchs_pca.coefs, MN, P);iddico = reshape(patchs_pca.iddico, MN, 1); % iddico很奇怪，其所有值全部为1而已elseisimage = 0;[MN,P] = size(patchs_pca.coefs);coefs = patchs_pca.coefs;iddico = patchs_pca.iddico;end% (49,49) -> 49P = size(patchs_pca.dicos{1}.axis, 1);% 1L = length(patchs_pca.dicos);% 初始化待重构的图片所有像素值为0patchs = zeros(MN, P);for i = 1:L% 【（256036,1）* （1,256036）的转置 】的转置= （256036,1）的转置 = （1,256036）% 这个到底在说什么意思呢% 其实就是获取有效的索引，这里的索引对应的是从原图片中提取出来的所有patchidx = ((iddico == i) .* (1:(MN))')';% ？应该都是大于0的吧idx = idx(idx > 0);K = size(idx, 2); % 有效索引的个数subK = min(K, 10000);k = 1;% 迭代重建过程：疑问的是这里为什么是从2开始的？% （1：1000) + 1 ==> (2: 1001)% (1: 1000) + 246035(K - subK - 1) ==> (K - subK, K - 1)while k < K - subK% (1,1000)range = (1:subK) + k;% 按顺序依次获取一部分patch, 这里对coefs是进行行索引subcoefs = coefs(idx(range), :);% 个人理解应该是将新坐标变换回旧坐标 并加上相应的均值patchs(idx(range), :) = ...subcoefs * patchs_pca.dicos{i}.axis' + ... % (1000,49) * (49, 49)ones(size(range, 2), 1) * patchs_pca.dicos{i}.mean; % (1000,1) * (1,49)%repmat(patchs_pca.dicos{i}.mean, size(range, 2), 1);clear subcoefs;k = k + subK;end% 对剩下长度不足subKd的所有patch来进行重建if k <= Krange = (k:K);subcoefs = coefs(idx(range), :);patchs(idx(range), :) = ...subcoefs * patchs_pca.dicos{i}.axis' + ...ones(size(range, 2), 1) * patchs_pca.dicos{i}.mean;%repmat(patchs_pca.dicos{i}.mean, size(range, 2), 1);clear subcoefs;endendclear coefs;clear iddico;if isimagepatchs = reshape(patchs, M, N, P); % （506,506,49（end
[4]重点是叠加像素值然后求平均值
function ima = reprojection_UWA(ima_patchs,xg,yg)%reprojection_UWA compute uniform weight reprojections from
% patches to pixels values
%
% INPUT:
% ima_patchs : values of the collection of patches
% xg, yg : Initial values of the image/normalization, default are
% xg = zeros(M,N);
% yg = zeros(M,N);
% OUTPUT:
% ima : image in the original domain
%
%ima = reprojection_UWA(ima_patchs,xg,yg)
% computes the pixels values knowing the values of the whole collections of
% the patches of an image. The reprojection is uniform.
%
%
% Copyright (C) 2011 GP-PCA project
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)
%
%---------------------------------------------------------------------
%
% This file is part of GP-PCA.
%
% GP-PCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as
% published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% GP-PCA is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public
% License along with GP-PCA. If not, see
% <http://www.gnu.org/licenses/>.
% Charles Deledalle, Joseph Salmon, Arnak S. Dalalyan
%
% See The GNU Public License (GPL)[M, N, P] = size(ima_patchs);if nargin <= 2 %判断有几个输入参数% 感觉这里xg和yg都没有什么用，因为后面根本用不到，就算用到了值也全部是0，没有发生任何更新xg = zeros(M,N);yg = zeros(M,N);endp = sqrt(P);ima = zeros(M+p-1, N+p-1);norm = zeros(M+p-1, N+p-1);% 就是把去噪后的patch依次叠加在同原始图片一样大的图片画布上% 并且统计每个像素点的值是来自多少个patch的叠加% 然后进行一个平均就可以了for i = 1:Mfor j = 1:Nxrange = mod(round((i-1)+(1:p)+xg(i,j))-1,M+p-1)+1;%（i,i+p-1)yrange = mod(round((j-1)+(1:p)+yg(i,j))-1,N+p-1)+1;% (j, j+p-1)ima(xrange, yrange) = ...ima(xrange, yrange) + ...reshape(ima_patchs(i,j,:), p, p);norm(xrange, yrange) = ...norm(xrange, yrange) + ...1;endendima = ima ./ norm;clear norm;
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