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📋📋📋本文目录如下：🎁🎁🎁
目录
💥1 概述
文献来源：
本文介绍了一种基于时空总变化的高光谱去噪算法。去噪问题被表述为混合降噪问题。已经考虑了一种通用噪声模型，该模型不仅考虑了高斯噪声，还考虑了稀疏噪声。利用空间维度的二维总变化和光谱维度上的一维总变化，利用了高光谱图像的固有结构。去噪问题被表述为一个优化问题，其解决方案是使用分裂布雷格曼方法推导的。实验结果表明，所提算法能够显著降低真实噪声高光谱图像的噪声。所提出的算法已与现有的先进方法进行了比较。定量和定性结果表明，所提算法在峰值信噪比、结构相似性和视觉质量方面具有优越性。
📚2 运行结果
部分代码：
%% Some initializations
[m,n,dim]=size(noisy); mn=m*n;
y=reshape(noisy,mn*dim,1);
b1=zeros(mn*dim,1); x=y;b2=b1; p=b1;q=b1; s=b1;
% Make total variation matrix
Dh=TVmatrix(m,n,'H');
Dv=TVmatrix(m,n,'V');
D=opTV1(dim);D=D';
D1=kron(D',Dh); D2=kron(D',Dv);
%D1=KronProd({Dh,D'}); D2=KronProd({Dv,D'});
%% Main iteration
for i=1:maxiter
%solve subproblem for x
bigY=(y-s)+nu*D1'*(p-b1)+nu*D2'*(q-b2);
[x,~]=lsqr(@afun,bigY,1e-15,10,[],[],x);
p=SoftTh(D1*x+b1,mu/nu);
q=SoftTh(D2*x+b2,mu/nu);
s=SoftTh(y-x,lambda);
%Update B1,B2 and B3
b1=b1+D1*x-p;
b2=b2+D2*x-q;
if rem(i,10)==0
fprintf('%d iterations done of %d \n ',i,maxiter);
end
end
denoised=reshape(x,m,n,dim);
%% This is a function handle used in LSQR
function y = afun(x,str)
tempval= nu*((D1'*(D1*x))+(D2'*(D2*x)))+ x;
switch str
case 'transp'
y = tempval;
case 'notransp'
y = tempval;
end
end
end
%% Soft Thresholding
function X=SoftTh(B,lambda)
X=sign(B).*max(0,abs(B)-(lambda/2));
end
%% Total Variation
%This function will generate total variation operator for an image of size
%mxn. Both horizontal and vertical total variation operators can be made
%using this code.
function opD=TVmatrix(m,n,str)
if str=='H' % This will give matrix for Horizontal Gradient
D = spdiags([-ones(n,1) ones(n,1)],[0 1],n,n);
D(n,:) = 0;
D = kron(D,speye(m));
elseif str=='V' %This will give matrix for Verticle Gradient
D = spdiags([-ones(m,1) ones(m,1)],[0 1],m,m);
D(m,:) = 0;
D = kron(speye(n),D);
end
opD=D;
end
%% This function will generate total variation operator for 1D signals
function opD=opTV1(m)
%Make two vectors of elements -1 and 1 of lengths (m-1)
B=[ -1*ones(m-1,1),ones(m-1,1)];
%Make sparse diagonal matrix D of size m-1 by m
%with -1's on zeroth diagonal and 1's on 1st diagonal;
D=spdiags(B,[0,1],m-1,m);
🎉3 参考文献
部分理论来源于网络，如有侵权请联系删除。
[1]H. K. Aggarwal and A. Majumdar, "Hyperspectral Image Denoising Using Spatio-Spectral Total Variation," in IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 3, pp. 442-446, March 2016, doi: 10.1109/LGRS.2016.2518218.