图像去噪序列——BM3D图像去噪模型实现

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1. BM3D模型简介

BM3D模型是一个两阶段图像去噪方法，主要包含两个步骤:

(1) 在噪声图像上，利用局部区域搜索相似块，并进行堆叠，在变换域(DCT域、FFT域）利用硬阈值去噪方法对堆叠的图像块进行去噪，获得堆叠相似块的估计值，最后，根据均值权重进行聚合；

(2) 通过步骤(1) 获取初步估计的图像，在初步估计的图像上进行相似块的聚合；然后，利用维纳协同滤波进行图像去噪，从而，获取最后的去噪结果

图像去噪序列——BM3D图像去噪模型实现

2. 模型实现(代码参考网络实现)：

% BM3D_Color_Demo 
% BM3D 在彩色图像上去噪
% Author: HSW
% Date: 2018-05-06 
%

clc; 
close all; 
clear all; 

img_org = imread('timg.png'); 

figure(1); 
imshow(img_org); 
title('原图像'); 

% 加噪声
sigma = 25; 
img_noise = double(img_org)+sigma * randn(size(img_org));

figure; 
imshow(img_noise / 255, []); 
title('噪声图像'); 

img_denoise = BM3D_Color(img_noise, 0, sigma, 0, 1); 

figure; 
imshow(img_denoise / 255, []); 
title('去噪图像');

% BM3D_Gray_Demo
% BM3D 在灰度图像上去噪
% Author: HSW
% Date: 2018-05-06 
% 

clc; 
close all; 
clear all; 

img_org = imread('timg.png');

img_gray = rgb2gray(img_org); 

figure(1); 
imshow(img_gray); 
title('原图像'); 

% 加噪声
sigma = 25; 
img_noise = double(img_gray)+sigma * randn(size(img_gray));

figure; 
imshow(img_noise / 255, []); 
title('噪声图像'); 

img_denoise = BM3D_Gray(img_noise, 0, sigma, 1); 

figure; 
imshow(img_denoise / 255, []); 
title('去噪图像');

function img_denoise = BM3D_Color(img_noise, tran_mode, sigma, color_mode, isDisplay)
% BM3D实现去噪
% Inputs:
%       img_noise: 噪声图像
%       tran_mode: 变换方法： 默认值为0, tran_mode: = 0, fft; = 1, dct; = 2, dwt, = 3, db1
%       sigma: 噪声水平，默认值为10
%       color_mode: 彩色图像去噪时采用的颜色空间, 默认值为0, color_mode: = 0, YUV; = 1, YCbCr; = 2, OPP
%  Ouputs:
%       img_out: 去噪图像
% 参考文献：An Analysis and Implementation of the BM3D Image Denoising Method
% Inputs:
%        img_in: 噪声图像，必须为矩形方阵
%        tran_mode: = 0, FFT; = 1, DCT; = 2, DWT, = 3, db1
% Outputs:
%        img_denoise: 去噪图像
%
%
if ~exist('isDisplay', 'var')
    isDisplay = 0;
end

if ~exist('color_mode', 'var')
    color_mode = 0;
end

if ~exist('sigma', 'var')
    sigma = 10;
end

if ~exist('tran_mode', 'var')
    tran_mode = 0;
end

[row, col, dims] = size(img_noise);

img_trans = rgb2other(img_noise, color_mode);

% First Step 参数
kHard           = 8;          % 块大小
pHard           = 4;          % 块移动间隔
lambda_distHard = 0;          % 求相似的距离时，变换后，收缩的阈值
nHard           = 40;         % 搜索窗口大小
NHard           = 28;         % 最多相似块个数
tauHard         = 5000;       % 最大的相似距离for fft

% kaiser窗口的参数，实际上并没有特别大的影响
beta=2;
Wwin2D = kaiser(kHard, beta) * kaiser(kHard, beta)';

% Second Step参数
kWien           = kHard;
pWien           = pHard;
lambda_distWien = lambda_distHard;
nWien           = nHard;
NWien           = NHard;
tauWien         = tauHard;
sigma2          = sigma*sigma;

if tran_mode == 0
    % FFT
    lambda2d=400;
    lambda1d=500;
    lambda2d_wie=50;
    lambda1d_wie=500;
elseif tran_mode == 1
    % DCT
    lambda2d=50;
    lambda1d=80;
    lambda2d_wie=20;
    lambda1d_wie=60;
elseif tran_mode == 2
    % DWT
    lambda2d=50;
    lambda1d=80;
    lambda2d_wie=20;
    lambda1d_wie=60;
end

fprintf('BM3D: First Stage Start...\n');
%block为原始图像块， tran_block为FFT变换且硬阈值截断后的频域系数(频域， 计算距离的时候采用的是变换块)
[block_ch1, tran_block_ch1, block2row_idx_ch1, block2col_idx_ch1] = im2block(img_trans(:,:,1), kHard, pHard, lambda_distHard, 0);
[block_ch2, tran_block_ch2, block2row_idx_ch2, block2col_idx_ch2] = im2block(img_trans(:,:,2), kHard, pHard, lambda_distHard, 0); 
[block_ch3, tran_block_ch3, block2row_idx_ch3, block2col_idx_ch3] = im2block(img_trans(:,:,3), kHard, pHard, lambda_distHard, 0); 

%bn_r和bn_c为行和列上的图像块个数
bn_r = floor((row - kHard) / pHard) + 1;
bn_c = floor((col - kHard) / pHard) + 1;
%基础估计的图像
img_basic_sum = zeros(row, col, 3);
img_basic_weight = zeros(row, col, 3);
%对每个块遍历
for i=1:bn_r
    for j=1:bn_c
        
        % 利用亮度通道进行相似块搜索
        [sim_blk_ch1, sim_num, sim_blk_idx] = search_similar_block(i, j, block_ch1, tran_block_ch1, floor(nHard/pHard), bn_r, bn_c, tauHard, NHard);
        
        % 进行亮度通道处理
        % 协同滤波： 公式(2)
        tran3d_blk_shrink_ch1 = transform_3d(sim_blk_ch1, tran_mode, lambda2d, lambda1d);
        tran3d_blk_shrink_ch2 = transform_3d(block_ch2(:,:,sim_blk_idx), tran_mode, lambda2d, lambda1d); 
        tran3d_blk_shrink_ch3 = transform_3d(block_ch3(:,:,sim_blk_idx), tran_mode, lambda2d, lambda1d); 
        % 聚合： 公式(3)中的说明
        NHard_P_ch1 = nnz(tran3d_blk_shrink_ch1);
        NHard_P_ch2 = nnz(tran3d_blk_shrink_ch2); 
        NHard_P_ch3 = nnz(tran3d_blk_shrink_ch3); 
        
        if NHard_P_ch1 > 1
            wHard_P_ch1 = 1 / NHard_P_ch1;
        else
            wHard_P_ch1 = 1;
        end
        
        if NHard_P_ch2 > 1
            wHard_P_ch2 = 1 / NHard_P_ch2; 
        else
            wHard_P_ch2 = 1; 
        end 
        
        if NHard_P_ch3 > 1
            wHard_P_ch3 = 1 / NHard_P_ch3; 
        else
            wHard_P_ch3 = 1; 
        end 
        
        blk_est_ch1 = inv_transform_3d(tran3d_blk_shrink_ch1,tran_mode);
        blk_est_ch1 = real(blk_est_ch1);
        
        blk_est_ch2 = inv_transform_3d(tran3d_blk_shrink_ch2, tran_mode); 
        blk_est_ch2 = real(blk_est_ch2); 
        
        blk_est_ch3 = inv_transform_3d(tran3d_blk_shrink_ch3, tran_mode); 
        blk_est_ch3 = real(blk_est_ch3); 
        
        % 公式(3): 对亮度通道，即第1个通道
        for k=1:sim_num
            idx = sim_blk_idx(k);
            ir = block2row_idx_ch1(idx);
            jr = block2col_idx_ch1(idx);
            img_basic_sum(ir:ir+kHard-1, jr:jr+kHard-1, 1) = img_basic_sum(ir:ir+kHard-1, jr:jr+kHard-1, 1) + wHard_P_ch1 * blk_est_ch1(:, :, k);
            img_basic_weight(ir:ir+kHard-1, jr:jr+kHard-1, 1) = img_basic_weight(ir:ir+kHard-1, jr:jr+kHard-1, 1) + wHard_P_ch1;
            
            img_basic_sum(ir:ir+kHard-1, jr:jr+kHard-1, 2) = img_basic_sum(ir:ir+kHard-1, jr:jr+kHard-1, 2) + wHard_P_ch2 * blk_est_ch2(:, :, k);
            img_basic_weight(ir:ir+kHard-1, jr:jr+kHard-1, 2) = img_basic_weight(ir:ir+kHard-1, jr:jr+kHard-1, 2) + wHard_P_ch2;
            
            img_basic_sum(ir:ir+kHard-1, jr:jr+kHard-1, 3) = img_basic_sum(ir:ir+kHard-1, jr:jr+kHard-1, 3) + wHard_P_ch3 * blk_est_ch3(:, :, k);
            img_basic_weight(ir:ir+kHard-1, jr:jr+kHard-1, 3) = img_basic_weight(ir:ir+kHard-1, jr:jr+kHard-1, 3) + wHard_P_ch3;
        end
        
    end
end

img_basic = img_basic_sum ./ img_basic_weight;

if isDisplay
    figure;
    img_rgb = other2rgb(img_basic, color_mode); 
    imshow(img_rgb / 255.0 ,[]);
    title('BM3D:Fist Stage Result');
end

fprintf('BM3D: First Stage End...\n');

fprintf('BM3D: Second Stage Start...\n');

[block_basic_ch1,tran_block_basic_ch1,block2row_idx_basic_ch1,block2col_idx_basic_ch1] = im2block(img_basic(:, :, 1), kWien, pWien, lambda_distWien, 0);
[block_basic_ch2,tran_block_basic_ch2,block2row_idx_basic_ch3,block2col_idx_basic_ch2] = im2block(img_basic(:, :, 2), kWien, pWien, lambda_distWien, 0);
[block_basic_ch3,tran_block_basic_ch3,block2row_idx_basic_ch3,block2col_idx_basic_ch3] = im2block(img_basic(:, :, 3), kWien, pWien, lambda_distWien, 0);

bn_r = floor((row - kWien) / pWien) + 1;
bn_c = floor((col - kWien) / pWien) + 1;

img_wien_sum = zeros(row, col, 3);
img_wien_weight = zeros(row, col, 3);

for i=1:1:bn_r
    for j=1:1:bn_c
        % 公式(5), 利用亮度进行相似性搜索
        [sim_blk_basic_ch1, sim_num, sim_blk_basic_idx] = search_similar_block(i, j, block_basic_ch1, tran_block_basic_ch1, floor(nWien/pWien), bn_r, bn_c, tauWien, NWien);
        
        % 公式(6)
        tran3d_blk_basic_ch1 = transform_3d(sim_blk_basic_ch1, tran_mode, lambda2d_wie, lambda1d_wie);
        tran3d_blk_basic_ch2 = transform_3d(block_basic_ch2(:, :, sim_blk_basic_idx), tran_mode, lambda2d_wie, lambda1d_wie); 
        tran3d_blk_basic_ch3 = transform_3d(block_basic_ch3(:, :, sim_blk_basic_idx), tran_mode, lambda2d_wie, lambda1d_wie); 
        
        omega_P_ch1 = (tran3d_blk_basic_ch1.^2) ./ ((tran3d_blk_basic_ch1.^2) + sigma2);
        omega_P_ch2 = (tran3d_blk_basic_ch2.^2) ./ ((tran3d_blk_basic_ch2.^2) + sigma2); 
        omega_P_ch3 = (tran3d_blk_basic_ch3.^2) ./ ((tran3d_blk_basic_ch3.^2) + sigma2); 
        
        % 公式(7)
        tran3d_blk_ch1 = transform_3d(block_ch1(:, :, sim_blk_basic_idx), tran_mode, lambda2d_wie, lambda1d_wie);
        tran3d_blk_ch2 = transform_3d(block_ch2(:, :, sim_blk_basic_idx), tran_mode, lambda2d_wie, lambda1d_wie); 
        tran3d_blk_ch3 = transform_3d(block_ch3(:, :, sim_blk_basic_idx), tran_mode, lambda2d_wie, lambda1d_wie); 
        
        blk_est_ch1 = inv_transform_3d(omega_P_ch1 .* tran3d_blk_ch1, tran_mode);
        blk_est_ch2 = inv_transform_3d(omega_P_ch2 .* tran3d_blk_ch2, tran_mode); 
        blk_est_ch3 = inv_transform_3d(omega_P_ch3 .* tran3d_blk_ch3, tran_mode); 
        
        blk_est_ch1 = real(blk_est_ch1);
        blk_est_ch2 = real(blk_est_ch2); 
        blk_est_ch3 = real(blk_est_ch3); 
        
        NWien_P_ch1 = nnz(omega_P_ch1);
        NWien_P_ch2 = nnz(omega_P_ch2); 
        NWien_P_ch3 = nnz(omega_P_ch3); 
        
        if NWien_P_ch1 > 1
            wWien_P_ch1 = 1 / (NWien_P_ch1);
        else
            wWien_P_ch1 = 1;
        end
        
        if NWien_P_ch2 > 1
            wWien_P_ch2 = 1/(NWien_P_ch2);
        else
            wWien_P_ch2 = 1;
        end
        
        if NWien_P_ch3 > 1
            wWien_P_ch3 = 1 / (NWien_P_ch3);
        else
            wWien_P_ch3 = 1;
        end
        % 公式(8)
        for k=1:sim_num
            idx=sim_blk_basic_idx(k);
            ir=block2row_idx_basic_ch1(idx);
            jr=block2col_idx_basic_ch1(idx);
            img_wien_sum(ir:ir+kWien-1, jr:jr+kWien-1, 1) = img_wien_sum(ir:ir+kWien-1, jr:jr+kWien-1, 1) + wWien_P_ch1 * blk_est_ch1(:, :, k);
            img_wien_weight(ir:ir+kWien-1, jr:jr+kWien-1, 1) = img_wien_weight(ir:ir+kWien-1, jr:jr+kWien-1, 1) + wWien_P_ch1;
            
            img_wien_sum(ir:ir+kWien-1, jr:jr+kWien-1, 2) = img_wien_sum(ir:ir+kWien-1, jr:jr+kWien-1, 2) + wWien_P_ch2 * blk_est_ch2(:, :, k);
            img_wien_weight(ir:ir+kWien-1, jr:jr+kWien-1, 2) = img_wien_weight(ir:ir+kWien-1, jr:jr+kWien-1, 2) + wWien_P_ch2;
            
            img_wien_sum(ir:ir+kWien-1, jr:jr+kWien-1, 3) = img_wien_sum(ir:ir+kWien-1, jr:jr+kWien-1, 3) + wWien_P_ch3 * blk_est_ch3(:, :, k);
            img_wien_weight(ir:ir+kWien-1, jr:jr+kWien-1, 3) = img_wien_weight(ir:ir+kWien-1, jr:jr+kWien-1, 3) + wWien_P_ch3;
        end
    end
end

img_other = img_wien_sum ./ img_wien_weight; 
img_denoise = other2rgb(img_other, color_mode);

fprintf('BM3D: Second Stage End\n');

function img_denoise = BM3D_Gray(img_noise, tran_mode, sigma, isDisplay)
% 参考文献：An Analysis and Implementation of the BM3D Image Denoising Method
% Inputs:
%        img_noise: 灰度噪声图像，必须为矩形方阵
%        tran_mode: = 0, fft; = 1, dct; = 2, dwt, = 3, db1
% Outputs:
%        img_denoise: 去噪图像
%
if ~exist('tran_mode', 'var')
    tran_mode = 0;
end

if ~exist('sigma', 'var')
    sigma = 10;
end

if ~exist('isDisplay', 'var')
    isDisplay = 0;
end

[row,col] = size(img_noise);

% First Step 参数
kHard           = 8;          % 块大小
pHard           = 4;          % 块移动间隔
lambda_distHard = 0;          % 求相似的距离时，变换后，收缩的阈值
nHard           = 40;         % 搜索窗口大小
NHard           = 28;         % 最多相似块个数
tauHard         = 5000;       % 最大的相似距离for fft

% kaiser窗口的参数，实际上并没有特别大的影响
beta=2;
Wwin2D = kaiser(kHard, beta) * kaiser(kHard, beta)';

% Second Step参数
kWien           = kHard;
pWien           = pHard;
lambda_distWien = lambda_distHard;
nWien           = nHard;
NWien           = NHard;
tauWien         = tauHard;
sigma2          = sigma*sigma;

if(tran_mode==0)        %fft
    lambda2d=400;
    lambda1d=500;
    lambda2d_wie=50;
    lambda1d_wie=500;
elseif(tran_mode == 1)  %dct
    lambda2d=50;
    lambda1d=80;
    lambda2d_wie=20;
    lambda1d_wie=60;
elseif(tran_mode == 2)  %dwt
    lambda2d=50;
    lambda1d=80;
    lambda2d_wie=20;
    lambda1d_wie=60;
end

%block为原始图像块， tran_block为FFT变换且硬阈值截断后的频域系数(频域， 计算距离的时候采用的是变换块)
[block,tran_block,block2row_idx,block2col_idx]=im2block(img_noise,kHard,pHard,lambda_distHard,0);

%bn_r和bn_c为行和列上的图像块个数
bn_r=floor((row-kHard)/pHard)+1;
bn_c=floor((col-kHard)/pHard)+1;
%基础估计的图像
img_basic_sum=zeros(row,col);
img_basic_weight=zeros(row,col);
%basic处理
fprintf('BM3D: First Stage Start...\n');
%对每个块遍历
for i=1:bn_r
    for j=1:bn_c
        [sim_blk,sim_num,sim_blk_idx]=search_similar_block(i,j,block,tran_block,floor(nHard/pHard),bn_r,bn_c,tauHard,NHard);
        % 协同滤波： 公式(2)
        tran3d_blk_shrink=transform_3d(sim_blk,tran_mode,lambda2d,lambda1d);
        % 聚合： 公式(3)中的说明
        NHard_P=nnz(tran3d_blk_shrink);
        if(NHard_P >1)
            wHard_P=1/NHard_P;
        else
            wHard_P=1;
        end
        blk_est =inv_transform_3d(tran3d_blk_shrink,tran_mode);
        blk_est=real(blk_est);
        
        % 公式(3)
        for k=1:sim_num
            idx=sim_blk_idx(k);
            ir=block2row_idx(idx);
            jr=block2col_idx(idx);
            img_basic_sum(ir:ir+kHard-1,jr:jr+kHard-1) = img_basic_sum(ir:ir+kHard-1,jr:jr+kHard-1) + wHard_P*blk_est(:,:,k);
            img_basic_weight(ir:ir+kHard-1,jr:jr+kHard-1) = img_basic_weight(ir:ir+kHard-1,jr:jr+kHard-1) + wHard_P;
        end
    end
end
fprintf('BM3D: First Stage End...\n');
img_basic=img_basic_sum./img_basic_weight;

if isDisplay
    figure;
    imshow(img_basic,[]);
    title('BM3D:Fist Stage Result');
end


[block_basic,tran_block_basic,block2row_idx_basic,block2col_idx_basic] = im2block(img_basic,kWien,pWien,lambda_distWien,0);
bn_r=floor((row-kWien)/pWien)+1;
bn_c=floor((col-kWien)/pWien)+1;
img_wien_sum=zeros(row,col);
img_wien_weight=zeros(row,col);

fprintf('BM3D: Second Stage Start...\n');
for i=1:1:bn_r
    for j=1:1:bn_c
        % 公式(5)
        [sim_blk_basic,sim_num,sim_blk_basic_idx] = search_similar_block(i,j,block_basic,tran_block_basic,floor(nWien/pWien),bn_r,bn_c,tauWien,NWien);
        % 公式(6)
        tran3d_blk_basic = transform_3d(sim_blk_basic,tran_mode,lambda2d_wie,lambda1d_wie);
        omega_P=(tran3d_blk_basic.^2)./((tran3d_blk_basic.^2)+sigma2);
        % 公式(7)
        tran3d_blk = transform_3d(block(:,:,sim_blk_basic_idx),tran_mode,lambda2d_wie,lambda1d_wie);
        blk_est=inv_transform_3d(omega_P.*tran3d_blk,tran_mode);
        blk_est=real(blk_est);
        NWien_P=nnz(omega_P);
        if(NWien_P >1)
            wWien_P=1/(NWien_P);
        else
            wWien_P=1;
        end
        % 公式(8)
        for k=1:sim_num
            idx=sim_blk_basic_idx(k);
            ir=block2row_idx_basic(idx);
            jr=block2col_idx_basic(idx);
            img_wien_sum(ir:ir+kWien-1,jr:jr+kWien-1) = img_wien_sum(ir:ir+kWien-1,jr:jr+kWien-1) + wWien_P*blk_est(:,:,k);
            img_wien_weight(ir:ir+kWien-1,jr:jr+kWien-1) = img_wien_weight(ir:ir+kWien-1,jr:jr+kWien-1) + wWien_P;
        end
    end
end
fprintf('BM3D: Second Stage End\n');

img_denoise = img_wien_sum./img_wien_weight;

function [block,transform_block,block2row_idx,block2col_idx] =im2block(img,k,p,lambda2D,delta)
% 实现图像分块
% Inputs：
%        k: 块大小
%        p: 块移动步长
%        lambda_2D: 收缩阈值
%        delta: 收缩阈值
%  Outputs:
%        block: 返回的块
%        transform_block: 变换后的块
%        block2row_idx: 块索引与图像块的左上角行坐标对应关系
%        block2col_idx: 块索引与图像块的左上角列坐标对应关系
%
[row,col] = size(img);
% 频域去噪中的硬阈值，实际上原文中，对于噪声方差小于40时thres = 0, 具体见公式(1)的说明第2点(即距离计算)
thres = lambda2D*delta*sqrt(2*log(row*col));
% r_num 和 c_num分别表示行和列上可以采集的块的数目
r_num = floor((row-k)/p)+1;
c_num = floor((col-k)/p)+1;
block = zeros(k,k,r_num*c_num);
block2row_idx = [];
block2col_idx = [];
cnt = 1;
for i = 0:r_num-1
    rs = 1+i*p;
    for j = 0:c_num-1
        cs = 1+j*p;
        block(:,:,cnt) = img(rs:rs+k-1,cs:cs+k-1);
        block2row_idx(cnt) = rs;
        block2col_idx(cnt) = cs;
        tr_b = fft2(block(:,:,cnt));
        idx = find(abs(tr_b)<thres);
        tr_b(idx) = 0;
        transform_block(:,:,cnt) = tr_b;
        cnt = cnt+1;
    end
end
end

function [blk_est]=inv_transform_3d(blk_tran3d,tran_mode)
% 3D 逆变换
% Inputs:
%       blk_tran3d: 在频域中，硬阈值滤波的图像块
%       tran_mode: 变换方法
% Outputs:
%       blk_est:
%
global blk_tran1d_s;
global blk_2d_s;
[m,n,blk_num]=size(blk_tran3d);

blk_invtran1d=zeros(m,n,blk_num);
blk_est=zeros(m,n,blk_num);

if(tran_mode==0)    %fft
    for i=1:1:m
        for j=1:1:n
            blk_invtran1d(i,j,:)=ifft(blk_tran3d(i,j,:));
        end
    end
    for i=1:1:blk_num
        blk_est(:,:,i)=ifft2(blk_invtran1d(:,:,i));
    end
elseif(tran_mode==1)  %dct
    for i=1:1:m
        for j=1:1:n
            blk_invtran1d(i,j,:)=idct(blk_tran3d(i,j,:));
        end
    end
    for i=1:1:blk_num
        blk_est(:,:,i)=idct2(blk_invtran1d(:,:,i));
    end
elseif(tran_mode==2)    %dwt
    blk_num=length(blk_2d_s);
    blk_c=waverec2(blk_tran3d,blk_tran1d_s,'haar');
    blk_est=[];
    for i=1:1:blk_num
        blk_est(:,:,i)=waverec2(blk_c(:,i),blk_2d_s{i},'Bior1.5');
    end
    
else
    error('tran_mode error');
end

end

function img_trans = other2rgb(img_in, color_mode)
% 将RGB颜色空间转为其他颜色空间
% Inputs:
%        img_in: RGB颜色空间图像
%        color_mode: 彩色图像去噪时采用的颜色空间, 默认值为0, color_mode: = 0, YUV; = 1, YCbCr; = 2, OPP
% Outputs:
%        img_trans: 其他颜色空间
%
% Author: HSW
% Date: 2018-05-06

img_trans = zeros(size(img_in));
[row, col, dims] = size(img_in);

if color_mode == 0
    color_tran = [0.30, 0.59, 0.11; -0.15, -0.29, 0.44; 0.61, -0.51, -0.10];
    color_tran_inv = inv(color_tran);
    for i = 1:row
        for j = 1:col
            other = [img_in(i, j, 1); img_in(i, j, 2); img_in(i, j, 3)];
            img_trans(i, j, :) = color_tran_inv * other;
        end
    end
elseif color_mode == 1
    color_tran = [0.30, 0.59, 0.11; -0.17, -0.33, 0.50; 0.50, -0.42, -0.08];
    color_tran_inv = inv(color_tran);
    for i = 1:row
        for j = 1:col
            other = [img_in(i, j, 1); img_in(i, j, 2); img_in(i, j, 3)];
            img_trans(i, j, :) = color_tran_inv * other;
        end
    end
elseif color_mode == 2
    color_tran = [1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0; 1.0 / 2.0, 0, -1.0 / 2.0; 1.0 / 4.0, -1.0 / 2.0, 1.0 / 4.0];
    color_tran_inv = inv(color_tran);
    for i = 1:row
        for j = 1:col
            other = [img_in(i, j, 1); img_in(i, j, 2); img_in(i, j, 3)];
            img_trans(i, j, :) = color_tran_inv * other;
        end
    end
end

end

function img_trans = rgb2other(img_in, color_mode)
% 将RGB颜色空间转为其他颜色空间
% Inputs:
%        img_in: RGB颜色空间图像
%        color_mode: 彩色图像去噪时采用的颜色空间, 默认值为0, color_mode: = 0, YUV; = 1, YCbCr; = 2, OPP
% Outputs:
%        img_trans: 其他颜色空间
%
% Author: HSW
% Date: 2018-05-06

img_trans = zeros(size(img_in));
[row, col, dims] = size(img_in);
if color_mode == 0
    color_tran = [0.30, 0.59, 0.11; -0.15, -0.29, 0.44; 0.61, -0.51, -0.10];
    for i = 1:row
        for j = 1:col
            rgb = [img_in(i, j, 1); img_in(i, j, 2); img_in(i, j, 3)]; 
            img_trans(i, j, :) = (color_tran * rgb)';
        end
    end
elseif color_mode == 1
    color_tran = [0.30, 0.59, 0.11; -0.17, -0.33, 0.50; 0.50, -0.42, -0.08];
    for i = 1:row
        for j = 1:col
            rgb = [img_in(i, j, 1); img_in(i, j, 2); img_in(i, j, 3)]; 
            img_trans(i, j, :) = (color_tran * rgb)';
        end
    end
elseif color_mode == 2
    color_tran = [1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0; 1.0 / 2.0, 0, -1.0 / 2.0; 1.0 / 4.0, -1.0 / 2.0, 1.0 / 4.0];
    for i = 1:row
        for j = 1:col
            rgb = [img_in(i, j, 1); img_in(i, j, 2); img_in(i, j, 3)]; 
            img_trans(i, j, :) = (color_tran * rgb)';
        end
    end
end

end

function [sim_blk,sim_num,sim_blk_idx]=search_similar_block(ik,jk,block,tran_block,np,bn_r,bn_c,tau,max_sim_num)
% 搜索相似块
% Inputs:
%       ik, jk： 待搜索相似块的索引
%       block: 图像块集合
%       tran_block： 图像块FFT硬阈值过滤后的FFT系数
%       k: 图像块大小
%       np: floor(nHard / pHard)， 其中nHard表示图像的搜索区域大小， pHard表示块的移动步长
%       bn_r, bn_c: 图像总的行/列可以采集图像块的数目
%       tau: 图像块相似性判断阈值，见公式(1)
%       max_sim_num: 最多保留相似块的数目
% Ouputs:
%       sim_blk:
%       sim_num:
%       sim_blk_idx:
%
% 搜索窗口的左上角，右下角的块索引
in_s = max(ik-floor(np/2),1);
jn_s = max(jk-floor(np/2),1);
in_e = min(ik+floor(np/2),bn_r);
jn_e = min(jk+floor(np/2),bn_c);
% 当前参考块
ref_blk = tran_block(:,:,((ik-1)*bn_c+jk));
ii = in_s:1:in_e;
jj = jn_s:1:jn_e;
[II,JJ] = meshgrid(ii,jj);
IDX = (II-1)*bn_c+JJ;
blk_idx=IDX(:);
% 收缩范围内的全部图像块
cur_blk=tran_block(:,:,blk_idx);
cnt=size(cur_blk,3);
ref_blk_mat=repmat(ref_blk,[1,1,cnt]);
delta_blk=cur_blk-ref_blk_mat;
dist=sum(sum(delta_blk.*delta_blk,1),2);
[dist_sort,dist_idx]=sort(dist);
% 最大相似块是真实相似块和目标参数相似块的最小值
max_num=min(cnt,max_sim_num);
if(dist_sort(max_num)<tau)
    sim_num=max_num;
else
    sim_num=sum(dist_sort(1:max_num)<tau);
end
cnt_idx=dist_idx(1:sim_num);
sim_blk_idx=blk_idx(cnt_idx);
sim_blk=block(:,:,sim_blk_idx);
end

function [val]=thres_shrink(data,thres)
% 进行阈值截断： 即 data(i) < thres ? data(i) = 0 : data(i) = data(i)
% Inputs:
%       data: 阈值截断前的数据
%       thres: 阈值
% Ouputs:
%       val: 阈值截断后的数据
% 
val=data;
idx=find(abs(data)<thres);
val(idx)=0;
end

function blk_tran3d = transform_3d(blk_3d,tran_mode,lambda2d,lambda1d)
% 进行3D变换，即Collaborative Filtering: 在图像块内进行2D变换，在图像块间进行1D变换
% 公式(2)
% Inputs:
%        blk_3d:
%        tran_mode:
% Ouputs:
%
global blk_tran1d_s;
global blk_2d_s;
[m,n,blk_num]=size(blk_3d);

%变换不同时，可能需要修改？？
blk_2d_shrink=zeros(m,n,blk_num);
blk_1d_shrink=zeros(m,n,blk_num);

if(tran_mode==0)    %fft
    for i=1:1:blk_num
        blk_tran2d = fft2(blk_3d(:,:,i));
        blk_2d_shrink(:,:,i) = thres_shrink(blk_tran2d,lambda2d);
    end
    for i=1:1:m
        for j=1:1:n
            blk_tran1d = fft(blk_2d_shrink(i,j,:));
            blk_1d_shrink(i,j,:) = thres_shrink(blk_tran1d,lambda1d);
        end
    end
    blk_tran3d=blk_1d_shrink;
    
elseif(tran_mode==1)  %dct
    for i=1:1:blk_num
        blk_tran2d=dct2(blk_3d(:,:,i));
        blk_2d_shrink(:,:,i)=thres_shrink(blk_tran2d,lambda2d);
    end
    for i=1:1:m
        for j=1:1:n
            blk_tran1d=dct(blk_2d_shrink(i,j,:));
            blk_1d_shrink(i,j,:)=thres_shrink(blk_tran1d,lambda1d);
        end
    end
    blk_tran3d=blk_1d_shrink;
    
elseif(tran_mode==2)    %dwt
    blk_2d_s={};
    blk_2d_shrink=[];%zeros()
    for i=1:1:blk_num
        [blk_tran2d_c,blk_tran2d_s]=wavedec2(blk_3d(:,:,i),2,'Bior1.5');
        blk_2d_shrink(:,i)=thres_shrink(blk_tran2d_c,lambda2d);
        blk_2d_s{i}=blk_tran2d_s;
    end
    %这里应该用 wavedec.因为是对1维？？
    [blk_tran1d_c,blk_tran1d_s]=wavedec2(blk_2d_shrink,1,'haar');
    blk_tran3d=thres_shrink(blk_tran1d_c,lambda1d);
    %   elseif(strcmp(tran_mode,'db1')) %还未实现
    %       blk_2d_s={};
    %       blk_2d_shrink=[];%zeros()
    %       for i=1:1:blk_num
    %           [blk_tran2d_cA,blk_tran2d_cH,blk_tran2d_cV,blk_tran2d_cD]=...
    %               dwt2(blk_3d(:,:,i),'db1');
    %           blk_2d_shrink(:,i)=thres_shrink(blk_tran2d_c,lambda2d);
    %           blk_2d_s{i}=blk_tran2d_s;
    %       end
    %       [blk_tran1d_c,blk_tran1d_s]=wavedec2(blk_2d_shrink,1,'haar');
    %       blk_tran3d=thres_shrink(blk_tran1d_c,lambda1d);
else
    error('tran_mode error');
end
end

3. 模型效果：

3.1 灰度图像

图像去噪序列——BM3D图像去噪模型实现