我想寫我自己的MATLAB代碼來計算逆氡變換(iradon),並且到目前爲止我已經成功地使用斜坡過濾器,海明窗口重建圖像,並且還基於Kak和Shakey的教科書,使用空間域中的一維投影與我的代碼中的窗口h的卷積。然而,我認爲如果我對窗口h進行FFT並將其乘以1D投影的FFT,我應該能夠獲得相同的重構。不幸的是,我所得到的是一團糟。在MATLAB中過濾反投影和設計濾波器
function [out] = myfbp4(arg2);
ph = phantom();
sino = radon(phantom,0:0.1:179);
rho2 = 183; % max rho
rho1 = -183; % min rho;
step = 1;
npos = 367;
dtheta = 0.1;
angles = deg2rad(0:dtheta:179);
nproj = length(angles);
n1 = ceil(log(npos)/log(2));
N = 2^n1; % smallest power of 2 greater than npos (for fft efficiency)
N = 1024; % for zero padding
fs = 1; % sampling frequency
T = 1; % sample spacing
% grid for reconstructed image
x1 = rho1:step:rho2;
y1 = rho1:step:rho2;
[yyy, xxx] = ndgrid(-y1, x1);
% build filter h according to Kak and Shakey
h = -floor(npos/2):T:floor(npos/2);
for i = 1:length(h)
if (mod(h(i),2) == 1)
h(i) = -1./(h(i)^2 * pi^2 * T^2);
else
h(i) = 0;
end
h(ceil(npos/2)) = 1/(4*T^2);
end
%%%%%%%%%%% RAMP FILTER %%%%%%%%%%%%%%%%
%%%%%%%%%% this is un needed when using h %%
%%%%%%%%%% see below... %%%%%%%%%%%%%%%%%%%%
rampFilterNum = [0:1:N/2-1 -N/2:1:-1];
rampFilterAbs = abs(rampFilterNum);
rampFilter = rampFilterAbs *fs/N;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% positions made to correspond to N point fft
drho = (rho2 - rho1)/(npos-1);
rho = rho1 + (0:(npos-1)) * drho;
positions = zeros(nproj, length(rho));
for i = 1:nproj,
positions(i, :) = rho;
end
if (strcmp(arg2,'filter'))
% compute FT of h and multiply by fft projections
fftProj = fft(sino, N);
hfft = fft(h,N);
fftProjFiltered = bsxfun(@times, hfft', fftProj);
ifftProj = real(ifft(fftProjFiltered));
filteredProjections = ifftProj;
end
if (strcmp(arg2,'conv'))
% make image my convolution of projections with h
for iproj = 1:nproj
sino(:, iproj) = conv(sino(:,iproj), h, 'same');
end
filteredProjections = sino;
end
% display the image through backprojection
fdata = zeros(size(xxx));
for iproj = 1:nproj
theta = angles(iproj);
rho1 = xxx*cos(theta) + yyy*sin(theta); % rotate coordinate system by theta
%r = x1;
r = positions(iproj,:);
fdata1 = filteredProjections(1:npos,iproj); % filtered projections
%fdata1 interp1(
fdata2 = interp1(r, fdata1, rho1, 'linear', 0);
fdata = fdata + deg2rad(dtheta) * fdata2; %theta*fdata2;
end
out = fdata;
end
剛用完= myfbp4('conv')或myfbp4('filter')會顯示不同的結果。看起來卷積工作正常,但過濾方法沒有按照我所希望的那樣工作。
任何人都可以看到問題嗎? (道歉,如果有任何多餘的代碼,我試圖削減它的大部分...我也應該提到,這個代碼是從某處借來的,並修改了一下,但我不記得我在哪裏找到它)。
在此先感謝
編輯:問題解決。問題在於我沒有取窗口h的傅立葉變換的絕對值來獲得頻率窗口。對於那些發現這一點的人來說,hfft = abs(fft(h,N))應該代替hfft = fft(h,N)。
您應該自己回答並將答案標記爲已接受,以便大家可以看到問題已解決。 http://stackoverflow.com/help/self-answer – Tapio