前面我們介紹了Lucy-Richardson的加速算法，這里給出其implement和PSF的顯微成像計算公式。

https://blog.csdn.net/weixin_41923961/article/details/81157082?

function result=Accelaration_DeconvLucy(data,psf,iteration,method) %----------------------------------------------- %Inputs: % data single diffraction limit image % psf PSF %iteration Maximum deconvolution iterations {example:20} %method accelarate method{'NoAcce'(normal),'Acce1','Acce2','Acce3'} %------------------------------------------------ %Output: % result Lucy-Richardson deconvolution result %------------------------------------------------ % reference: % [1].D. S. C. Biggs and M. Andrews, "Acceleration of iterative image restoration % algorithms," Appl. Opt. 36(8), 1766a€?1775 (1997).% Copyright 2018 Weisong Zhao et al % % This program 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. % % This program 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 this program. If not, see <http://www.gnu.org/licenses/>. psf= psf./sum(sum(psf)); psf0=psf; B=floor(max(size(data,1),size(data,2))/4); data=padarray(data, [B,B] , 'replicate'); % move the PSF so that the maximum is at pixel 1 in the corner psfm=psf; psf = zeros(size(data,1),size(data,2)); psf(1 : size(psfm,1), 1 : size(psfm,2)) = psfm; [~,idx] = max(psf(:)); [x,y,~] = ind2sub(size(psf), idx); psf = circshift(psf, -[x,y,1] + 1); otf = fftn(psf); fprintf('Start deconvolution\n') % Richardson Lucy update rule rliter = @(estimate, data, otf)fftn(data./ max(ifftn(otf .* fftn(estimate)), 1e-6)); switch methodcase'NoAcce'estimate=data;estimate=max(estimate,0.001);for iter = 1:iterationif mod(iter,10)==0fprintf('iteration %d \n',iter)endestimate= estimate.*ifftn(conj(otf).*rliter(estimate,data,otf));estimate=max(estimate,1e-5);% estimate=estimate./max(max(estimate));endresult=estimate(B:end-B, B:end-B)./max(max(estimate(B:end-B, B:end-B)));case 'Acce1'estimate=data;estimate=max(estimate,0.001);k=2;for iter = 1:iterationif mod(iter,10)==0fprintf('iteration %d \n',iter)endestimate= estimate.*(ifftn(conj(otf).*rliter(estimate,data,otf))).^k;% estimate=estimate./max(max(estimate));estimate=max(estimate,1e-5);endresult=estimate(B:end-B, B:end-B)./max(max(estimate(B:end-B, B:end-B)));case 'Acce2'estimate=data;estimate=max(estimate,0.001);delta=2;for iter = 1:iterationif mod(iter,10)==0fprintf('iteration %d \n',iter)endestimatek=estimate;estimate= estimate.*ifftn(conj(otf).*rliter(estimate,data,otf));between_k_and_k1=estimate-estimatek;estimate=estimate+delta*between_k_and_k1;estimate=max(estimate,0.00001);estimate=estimate./max(max(estimate));endresult=estimate(B:end-B, B:end-B)./max(max(estimate(B:end-B, B:end-B)));case 'Acce3'yk=data;xk=zeros(size(data));vk=zeros(size(data));for iter = 1:iterationxk_update=xk;xk= max(yk.*real(ifftn(conj(otf).*rliter(yk,data,otf)))./real(ifftn(fftn(ones(size(data))).*otf)),0.00001);vk_update=vk;vk=max(xk-yk,0.00001);if iter==1alpha=0;elsealpha=sum(sum(vk_update.*vk))/(sum(sum(vk_update.*vk_update))+eps);alpha=max(min(alpha,1),0);endyk=max(xk+alpha*(xk-xk_update),0.00001);endresult=yk(B+1:end-B, B+1:end-B)./max(max(yk(B+1:end-B, B+1:end-B))); end function Ipsf=Generate_PSF(pixel,lamda,NA,n,z) %----------------------------------------------- %Source code for generating PSF %pixel pixel size {example:65*10^-9} %lamda wavelength {example:532*10^-9} %NA NA {example:1.49} %n number of psf {example:64} %z defocus length {example:1*10^-6} %------------------------------------------------ %Output: % Ipsf PSF%------------------------------------------------------------------------------------- % Copyright 2018 Weisong Zhao % This program 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. % % This program 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 this program. If not, see <http://www.gnu.org/licenses/>. %------------------------------------------------------------------------------------- %% if nargin < 4 || isempty(n)n=32; end if nargin < 5 || isempty(z)z=0; end sin2=((1-(1-NA^2))/2); u=8*pi*z*sin2/lamda; h=@(r,p) 2*exp((1i*u*(p.^2))/2).*besselj(0,2*pi*r*NA/lamda.*p); x=-n*pixel:pixel:n*pixel; [X,Y]=meshgrid(x,x); [~,s1]=cart2pol(X,Y); idx=s1<=1; IP=zeros(size(X)); k=1; for f=1:1:size(s1)for j=1:1:size(s1)if idx(f,j)==0IP(f,j)=0;elseo=s1(idx);r=o(k);k=k+1;II=@(p)h(r,p);IP(f,j)=integral(II,0,1);endend end Ipsf=abs(IP.^2); Ipsf=Ipsf./sum(sum( Ipsf));

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