能否给我写一下它的matlab代码
时间: 2023-08-02 19:11:32 浏览: 49
当然可以,以下是Filtered Back Projection算法的Matlab代码实现:
``` matlab
function [img] = fbp(sinogram,theta,delta,filter_type)
% sinogram: 接收器接收到的投影数据
% theta: 接收器旋转的投影角度
% delta: 接收器旋转的角度间隔
% filter_type: 滤波器类型,可选'ram-lak','shepp-logan','cosine','hamming','hann'
% img: 重建后的图像
% 构造滤波器
n = size(sinogram,1);
if strcmp(filter_type,'ram-lak')
filter = abs(-n/2:n/2-1) / n;
elseif strcmp(filter_type,'shepp-logan')
filter = abs(-n/2:n/2-1) / n .* (0.54 + 0.46 * cos(2*pi*(-n/2:n/2-1)/n));
elseif strcmp(filter_type,'cosine')
filter = abs(-n/2:n/2-1) / n .* cos(pi*(-n/2:n/2-1)/n);
elseif strcmp(filter_type,'hamming')
filter = abs(-n/2:n/2-1) / n .* (0.54 + 0.46 * cos(2*pi*(-n/2:n/2-1)/n));
elseif strcmp(filter_type,'hann')
filter = abs(-n/2:n/2-1) / n .* (0.5 + 0.5 * cos(2*pi*(-n/2:n/2-1)/n));
else
error('Invalid filter type.')
end
% 进行滤波反投影
img = zeros(n);
[x,y] = meshgrid(-n/2+0.5:n/2-0.5,-n/2+0.5:n/2-0.5);
for i = 1:length(theta)
proj = sinogram(:,i);
if sum(proj) == 0
continue
end
proj = proj - mean(proj);
proj = proj .* filter';
proj_fft = fft(proj);
back_proj = real(ifft(proj_fft));
back_proj = back_proj(1:n);
coord = round(x*cos(theta(i)/180*pi) + y*sin(theta(i)/180*pi) + n/2);
valid_coord = find(coord > 0 & coord <= n);
img(sub2ind([n,n],coord(valid_coord),valid_coord)) = img(sub2ind([n,n],coord(valid_coord),valid_coord)) + back_proj(valid_coord);
end
img = img / delta;
end
```
使用方法示例:
``` matlab
% 生成样例数据
n = 512;
theta = 0:1:179;
delta = 1;
[x,y] = meshgrid(-n/2+0.5:n/2-0.5,-n/2+0.5:n/2-0.5);
img = phantom('Modified Shepp-Logan',n);
sinogram = radon(img,theta);
% 进行重建
img_fbp = fbp(sinogram,theta,delta,'ram-lak');
imshow(img_fbp,[]);
```
注意,这里只提供了一种常见的滤波器类型,如果需要使用其他滤波器类型,可根据需要自行修改代码。