I1=imread ('input1.jpg');
I2=imread ('input2.jpg');
I3=imread ('input3.jpg');
I1=rgb2gray(I1);
I2=rgb2gray(I2);
I3=rgb2gray(I3);
subplot(4,3,1),imshow(I1),title('输入图像1'),
subplot(4,3,2),imshow(I2),title('输入图像2'),
subplot(4,3,3),imshow(I3),title('输入图像3'),
% 计算图片数据的维数
[x1,y1,z1]=size(I1);
[x2,y2,z2]=size(I2);
[x3,y3,z3]=size(I3);
% 将其重新排列为一维行向量并组成矩阵
s1=[reshape(I1,[1,x1*y1*z1])];
s2=[reshape(I2,[1,x2*y2*z2])];
s3=[reshape(I3,[1,x3*y3*z3])];
S_all=[s1;s2;s3]; % 图片个数即为变量数，图片的像素数即为采样数
% 因此S_all是一个变量个数＊采样个数的矩阵
S=double(S_all); % 将图像数据转换为双精度格式 ，图片处理前要将数据格式用double转化为双精度格式（以保证计算精度）
Sweight=rand(size(S_all,1)); % 取一随机矩阵，作为信号混合的权矩阵 ，注意size(S_all,1)产生三个数
MixedS=Sweight*S; % 得到三个图像的混合信号矩阵
% 将混合矩阵重新排列为原始的图片矩阵并输出
ms1=reshape(MixedS(1,:),[x1,y1,z1]);
ms2=reshape(MixedS(2,:),[x2,y2,z2]);
ms3=reshape(MixedS(3,:),[x3,y3,z3]);
I1_mixed=uint8(round(ms1)); %显示图像前用uint8转换数据格式
I2_mixed=uint8(round(ms2));
I3_mixed=uint8(round(ms3));
subplot(4,3,4),imshow(I1_mixed),title('混合图像1'),
subplot(4,3,5),imshow(I2_mixed),title('混合图像2'),
subplot(4,3,6),imshow(I3_mixed),title('混合图像3'),
MixedS_bak=MixedS; % 将混合后的数据备份，以便在恢复时直接调用
%%%%%%%%%%%%%%%%%%%%%%%%%% 标准化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MixedS_mean=zeros(3,1);
for i=1:3
MixedS_mean(i)=mean(MixedS(i,:));
end % 计算MixedS的均值与方差
for i=1:3
for j=1:size(MixedS,2)
MixedS(i,j)=MixedS(i,j)-MixedS_mean(i);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%% 白化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MixedS_cov=cov(MixedS'); % cov为求协方差的函数
[E,D]=eig(MixedS_cov); % 对图片矩阵的协方差函数进行特征值分解
Q=inv(sqrt(D))*(E)'; % Q为白化矩阵
MixedS_white=Q*MixedS; % MixedS_white为白化后的图片矩阵
IsI=cov(MixedS_white'); % IsI应为单位阵
%%%%%%%%%%%%%%%%%%%%%%%% FASTICA算法 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
X=MixedS_white; % 以下算法将对X进行操作
[VariableNum,SampleNum]=size(X);
numofIC=VariableNum; % 在此应用中，独立元个数等于变量个数
B=zeros(numofIC,VariableNum); % 初始化列向量b的寄存矩阵,B=[b1,b2,...,bd]
for r=1:numofIC % 迭代求取每一个独立元
i=1;maxIterationsNum=150; % 设置最大迭代次数（即对于每个独立分量而言迭代均不超过此次数）
b=2*(rand(numofIC,1)-.5); % 随机设置b初值
b=b/norm(b); % 对b标准化
while i=maxIterationsNum+1
if i == maxIterationsNum % 循环结束处理
fprintf('\n第%d分量在%d次迭代内并不收敛。', r,maxIterationsNum);
break;
end
bOld=b; % 初始化前一步b的寄存器
u=1;
t=X'*b;
g=t.^3;
dg=3*t.^2;
b=((1-u)*t'*g*b+u*X*g)/SampleNum-mean(dg)*b;
% 核心公式，参见理论部分公式2.52
b=b-B*B'*b; % 对b正交化
b=b/norm(b);
if abs(abs(b'*bOld)-1)<1e-9 % 如果收敛，则
B(:,r)=b; % 保存所得向量b
break;
end
i=i+1;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%% 数据复原并构图 %%%%%%%%%%%%%%%%%%%%%%%%%%
ICAedS=B'*Q*MixedS_bak; % 参见理论部分公式2.55
ICAedS_bak=ICAedS;
ICAedS=abs(55*ICAedS);
% t1=ICAedS(1,:);
% t2=ICAedS(2,:);
% t3=ICAedS(3,:);
%
% for i=1:size(t1,2)
% t1(1,i)=t1(1,i)+abs(min(t1));
% t1(1,i)=t1(1,i)*256/(max(t1)-min(t1));
% t2(1,i)=t2(1,i)+abs(min(t2));
% t2(1,i)=t2(1,i)*256/(max(t2)-min(t2));
% t3(1,i)=t3(1,i)+abs(min(t3));
% t3(1,i)=t3(1,i)*256/(max(t3)-min(t3));
%
% end
%
% ICAedS(1,:)=t1;
% ICAedS(2,:)=t2;
% ICAedS(3,:)=t3;
% 将计算后的混合矩阵重新排列为图片矩阵并输出
is1=reshape(ICAedS(1,:),[x1,y1,z1]);
is2=reshape(ICAedS(2,:),[x2,y2,z2]);
is3=reshape(ICAedS(3,:),[x3,y3,z3]);
I1_icaed =uint8 (round(is1));
I2_icaed =uint8 (round(is2));
I3_icaed =uint8 (round(is3));
subplot(4,3,7),imshow(I1_icaed),title('ICA解混图像1'),
subplot(4,3,8),imshow(I2_icaed),title('ICA解混图像2'),
subplot(4,3,9),imshow(I3_icaed),title('ICA解混图像3'),
%%%%%%%%%%%%%%%%%%%%%%%%%% PCA计算并构图 %%%%%%%%%%%%%%%%%%%%%%%%%%
[V,D]=eig(MixedS_cov);
Vtmp=zeros(size(V,1),1);
for j=1:2
for i=1:2
if D(i,i)<D(i+1,i+1)
tmp=D(i,i);Vtmp=V(:,i);
D(i,i)=D(i+1,i+1);V(:,i)=V(:,i+1);
D(i+1,i+1)=tmp;V(:,i+1)=Vtmp;
end
end
end
t1=(MixedS'*V(:,1))';
t2=(MixedS'*V(:,2))';
t3=(MixedS'*V(:,3))';
for i=1:size(t1,2) % 亮度调整
t1(1,i)=t1(1,i)+abs(min(t1));
t1(1,i)=t1(1,i)*256/(max(t1)-min(t1));
t2(1,i)=t2(1,i)+abs(min(t2));
t2(1,i)=t2(1,i)*256/(max(t2)-min(t2));
t3(1,i)=t3(1,i)+abs(min(t3));
t3(1,i)=t3(1,i)*256/(max(t3)-min(t3));
end
%%%%%%%%%%%%%%%%%%%%%%% 构图 %%%%%%%%%%%%%%%%%%%%%%
ts1=reshape(t1,[x1,y1,z1]);
ts2=reshape(t2,[x2,y2,z2]);
ts3=reshape(t3,[x3,y3,z3]);
T1_icaed =uint8 (round(ts1));
T2_icaed =uint8 (round(ts2));
T3_icaed =uint8 (round(ts3));
subplot(4,3,10),imshow(T1_icaed),title('PCA解混图像1'),
subplot(4,3,11),imshow(T2_icaed),title('PCA解混图像2'),
subplot(4,3,12),imshow(T3_icaed),title('PCA解混图像3'),
%%%%%%%%%%%%%%%%%%%%%%%%%% 输出一维矢量图 %%%%%%%%%%%%%%%%%%%%%%%%%%
% subplot(3,3,1),plot(S(1,:)),title('输入图像1一维矢量图')
% subplot(3,3,2),plot(S(2,:)),title('输入图像2一维矢量图')
% subplot(3,3,3),plot(S(3,:)),title('输入图像3一维矢量图')
% subplot(3,3,4),plot(ICAedS(1,:)),title('ICA解混图像1一维矢量图')
% subplot(3,3,5),plot(ICAedS(2,:)),title('ICA解混图像2一维矢量图')
% subplot(3,3,6),plot(ICAedS(3,:)),title('ICA解混图像3一维矢量图')
% subplot(3,3,7),plot(t1),title('PCA解混图像1一维矢量图')
% subplot(3,3,8),plot(t2),title('PCA解混图像2一维矢量图')
% subplot(3,3,9),plot(t3),title('PCA解混图像3一维矢量图')
im = imread(imgname);
im=rgb2gray(im);
imnoise_1=imnoise(im,'speckle',1);
imnoise_1=uint8(imnoise_1);
g2=size(imnoise_1);
figure(2)imshow(imnoise_1);
title('Noise image');
imnoise_2=double(imnoise_1);
imnoise_3=imnoise_2+var;
imnoise_3=log(imnoise_3);
immoise_3=double(imnoise_3);
imnoise_4=exp(imnoise_3);
imnoise_4=imnoise_4-var;
imnoise_5=uint8(imnoise_4);
figure(5)imshow(imnoise_5)title('recovery speckle image');
end
I2=imread ('input2.jpg');
I3=imread ('input3.jpg');
I1=rgb2gray(I1);
I2=rgb2gray(I2);
I3=rgb2gray(I3);
subplot(4,3,1),imshow(I1),title('输入图像1'),
subplot(4,3,2),imshow(I2),title('输入图像2'),
subplot(4,3,3),imshow(I3),title('输入图像3'),
% 计算图片数据的维数
[x1,y1,z1]=size(I1);
[x2,y2,z2]=size(I2);
[x3,y3,z3]=size(I3);
% 将其重新排列为一维行向量并组成矩阵
s1=[reshape(I1,[1,x1*y1*z1])];
s2=[reshape(I2,[1,x2*y2*z2])];
s3=[reshape(I3,[1,x3*y3*z3])];
S_all=[s1;s2;s3]; % 图片个数即为变量数，图片的像素数即为采样数
% 因此S_all是一个变量个数＊采样个数的矩阵
S=double(S_all); % 将图像数据转换为双精度格式 ，图片处理前要将数据格式用double转化为双精度格式（以保证计算精度）
Sweight=rand(size(S_all,1)); % 取一随机矩阵，作为信号混合的权矩阵 ，注意size(S_all,1)产生三个数
MixedS=Sweight*S; % 得到三个图像的混合信号矩阵
% 将混合矩阵重新排列为原始的图片矩阵并输出
ms1=reshape(MixedS(1,:),[x1,y1,z1]);
ms2=reshape(MixedS(2,:),[x2,y2,z2]);
ms3=reshape(MixedS(3,:),[x3,y3,z3]);
I1_mixed=uint8(round(ms1)); %显示图像前用uint8转换数据格式
I2_mixed=uint8(round(ms2));
I3_mixed=uint8(round(ms3));
subplot(4,3,4),imshow(I1_mixed),title('混合图像1'),
subplot(4,3,5),imshow(I2_mixed),title('混合图像2'),
subplot(4,3,6),imshow(I3_mixed),title('混合图像3'),
MixedS_bak=MixedS; % 将混合后的数据备份，以便在恢复时直接调用
%%%%%%%%%%%%%%%%%%%%%%%%%% 标准化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MixedS_mean=zeros(3,1);
for i=1:3
MixedS_mean(i)=mean(MixedS(i,:));
end % 计算MixedS的均值与方差
for i=1:3
for j=1:size(MixedS,2)
MixedS(i,j)=MixedS(i,j)-MixedS_mean(i);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%% 白化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MixedS_cov=cov(MixedS'); % cov为求协方差的函数
[E,D]=eig(MixedS_cov); % 对图片矩阵的协方差函数进行特征值分解
Q=inv(sqrt(D))*(E)'; % Q为白化矩阵
MixedS_white=Q*MixedS; % MixedS_white为白化后的图片矩阵
IsI=cov(MixedS_white'); % IsI应为单位阵
%%%%%%%%%%%%%%%%%%%%%%%% FASTICA算法 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
X=MixedS_white; % 以下算法将对X进行操作
[VariableNum,SampleNum]=size(X);
numofIC=VariableNum; % 在此应用中，独立元个数等于变量个数
B=zeros(numofIC,VariableNum); % 初始化列向量b的寄存矩阵,B=[b1,b2,...,bd]
for r=1:numofIC % 迭代求取每一个独立元
i=1;maxIterationsNum=150; % 设置最大迭代次数（即对于每个独立分量而言迭代均不超过此次数）
b=2*(rand(numofIC,1)-.5); % 随机设置b初值
b=b/norm(b); % 对b标准化
while i=maxIterationsNum+1
if i == maxIterationsNum % 循环结束处理
fprintf('\n第%d分量在%d次迭代内并不收敛。', r,maxIterationsNum);
break;
end
bOld=b; % 初始化前一步b的寄存器
u=1;
t=X'*b;
g=t.^3;
dg=3*t.^2;
b=((1-u)*t'*g*b+u*X*g)/SampleNum-mean(dg)*b;
% 核心公式，参见理论部分公式2.52
b=b-B*B'*b; % 对b正交化
b=b/norm(b);
if abs(abs(b'*bOld)-1)<1e-9 % 如果收敛，则
B(:,r)=b; % 保存所得向量b
break;
end
i=i+1;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%% 数据复原并构图 %%%%%%%%%%%%%%%%%%%%%%%%%%
ICAedS=B'*Q*MixedS_bak; % 参见理论部分公式2.55
ICAedS_bak=ICAedS;
ICAedS=abs(55*ICAedS);
% t1=ICAedS(1,:);
% t2=ICAedS(2,:);
% t3=ICAedS(3,:);
%
% for i=1:size(t1,2)
% t1(1,i)=t1(1,i)+abs(min(t1));
% t1(1,i)=t1(1,i)*256/(max(t1)-min(t1));
% t2(1,i)=t2(1,i)+abs(min(t2));
% t2(1,i)=t2(1,i)*256/(max(t2)-min(t2));
% t3(1,i)=t3(1,i)+abs(min(t3));
% t3(1,i)=t3(1,i)*256/(max(t3)-min(t3));
%
% end
%
% ICAedS(1,:)=t1;
% ICAedS(2,:)=t2;
% ICAedS(3,:)=t3;
% 将计算后的混合矩阵重新排列为图片矩阵并输出
is1=reshape(ICAedS(1,:),[x1,y1,z1]);
is2=reshape(ICAedS(2,:),[x2,y2,z2]);
is3=reshape(ICAedS(3,:),[x3,y3,z3]);
I1_icaed =uint8 (round(is1));
I2_icaed =uint8 (round(is2));
I3_icaed =uint8 (round(is3));
subplot(4,3,7),imshow(I1_icaed),title('ICA解混图像1'),
subplot(4,3,8),imshow(I2_icaed),title('ICA解混图像2'),
subplot(4,3,9),imshow(I3_icaed),title('ICA解混图像3'),
%%%%%%%%%%%%%%%%%%%%%%%%%% PCA计算并构图 %%%%%%%%%%%%%%%%%%%%%%%%%%
[V,D]=eig(MixedS_cov);
Vtmp=zeros(size(V,1),1);
for j=1:2
for i=1:2
if D(i,i)<D(i+1,i+1)
tmp=D(i,i);Vtmp=V(:,i);
D(i,i)=D(i+1,i+1);V(:,i)=V(:,i+1);
D(i+1,i+1)=tmp;V(:,i+1)=Vtmp;
end
end
end
t1=(MixedS'*V(:,1))';
t2=(MixedS'*V(:,2))';
t3=(MixedS'*V(:,3))';
for i=1:size(t1,2) % 亮度调整
t1(1,i)=t1(1,i)+abs(min(t1));
t1(1,i)=t1(1,i)*256/(max(t1)-min(t1));
t2(1,i)=t2(1,i)+abs(min(t2));
t2(1,i)=t2(1,i)*256/(max(t2)-min(t2));
t3(1,i)=t3(1,i)+abs(min(t3));
t3(1,i)=t3(1,i)*256/(max(t3)-min(t3));
end
%%%%%%%%%%%%%%%%%%%%%%% 构图 %%%%%%%%%%%%%%%%%%%%%%
ts1=reshape(t1,[x1,y1,z1]);
ts2=reshape(t2,[x2,y2,z2]);
ts3=reshape(t3,[x3,y3,z3]);
T1_icaed =uint8 (round(ts1));
T2_icaed =uint8 (round(ts2));
T3_icaed =uint8 (round(ts3));
subplot(4,3,10),imshow(T1_icaed),title('PCA解混图像1'),
subplot(4,3,11),imshow(T2_icaed),title('PCA解混图像2'),
subplot(4,3,12),imshow(T3_icaed),title('PCA解混图像3'),
%%%%%%%%%%%%%%%%%%%%%%%%%% 输出一维矢量图 %%%%%%%%%%%%%%%%%%%%%%%%%%
% subplot(3,3,1),plot(S(1,:)),title('输入图像1一维矢量图')
% subplot(3,3,2),plot(S(2,:)),title('输入图像2一维矢量图')
% subplot(3,3,3),plot(S(3,:)),title('输入图像3一维矢量图')
% subplot(3,3,4),plot(ICAedS(1,:)),title('ICA解混图像1一维矢量图')
% subplot(3,3,5),plot(ICAedS(2,:)),title('ICA解混图像2一维矢量图')
% subplot(3,3,6),plot(ICAedS(3,:)),title('ICA解混图像3一维矢量图')
% subplot(3,3,7),plot(t1),title('PCA解混图像1一维矢量图')
% subplot(3,3,8),plot(t2),title('PCA解混图像2一维矢量图')
% subplot(3,3,9),plot(t3),title('PCA解混图像3一维矢量图')
im = imread(imgname);
im=rgb2gray(im);
imnoise_1=imnoise(im,'speckle',1);
imnoise_1=uint8(imnoise_1);
g2=size(imnoise_1);
figure(2)imshow(imnoise_1);
title('Noise image');
imnoise_2=double(imnoise_1);
imnoise_3=imnoise_2+var;
imnoise_3=log(imnoise_3);
immoise_3=double(imnoise_3);
imnoise_4=exp(imnoise_3);
imnoise_4=imnoise_4-var;
imnoise_5=uint8(imnoise_4);
figure(5)imshow(imnoise_5)title('recovery speckle image');
end