matlab实现平行束投影的FBP重建算法代码
时间: 2024-05-26 13:08:20 浏览: 24
FBP(Filtered Back Projection)是一种常用的计算机断层扫描(CT)重建算法,其主要思想是通过将每个探测器接收到的数据进行反投影,然后再对反投影后的数据进行滤波,最终得到图像。下面是Matlab实现平行束投影的FBP重建算法的代码:
```matlab
function [recon_image] = FBP_algorithm(projection_data, theta, detector_size, image_size, filter_type)
% projection_data: 投影数据
% theta: 投影角度
% detector_size: 探测器大小
% image_size: 重建图像大小
% filter_type: 滤波器类型,可以选择Ram-Lak、Shepp-Logan或Cosine等
% 设置重建图像像素大小和中心
recon_image = zeros(image_size);
center = (image_size + 1) / 2;
% 设置滤波器
filter_size = 2 * detector_size - 1;
filter = get_filter(filter_type, filter_size);
% 逐个角度进行反投影和滤波
for i = 1:length(theta)
projection = projection_data(:, i);
projection = [projection; zeros(detector_size - mod(length(projection), detector_size), 1)];
projection = reshape(projection, detector_size, []);
projection = fftshift(projection, 1);
projection = ifft(projection, [], 1);
projection = projection(1:detector_size/2+1, :);
projection = projection .* repmat(filter', size(projection, 1), 1);
projection = [projection; conj(flipud(projection(2:end-1, :)))];
projection = ifft(projection, [], 1);
projection = projection(1:detector_size, :);
projection = fftshift(projection, 1);
for j = 1:detector_size
angle = (j - center - 0.5) * pi / detector_size;
x = center + (center - j + 0.5) * tan(angle);
x1 = floor(x);
x2 = ceil(x);
if x1 >= 1 && x2 <= image_size
weight1 = x - x1;
weight2 = x2 - x;
recon_image(x1, i) = recon_image(x1, i) + weight1 * projection(j);
recon_image(x2, i) = recon_image(x2, i) + weight2 * projection(j);
end
end
end
end
function [filter] = get_filter(filter_type, filter_size)
if strcmp(filter_type, 'Ram-Lak')
filter = abs(-filter_size/2:filter_size/2-1)';
elseif strcmp(filter_type, 'Shepp-Logan')
w = abs(-filter_size/2:filter_size/2-1)';
filter = sin(pi * w / filter_size) ./ (pi * w / filter_size);
filter(filter_size/2+1) = 0;
elseif strcmp(filter_type, 'Cosine')
filter = cos(pi * (-filter_size/2:filter_size/2-1)' / filter_size);
else
error('Unsupported filter type');
end
end
```
相关问题:
1. FBP算法是什么?
2. FBP算法的主要思想是什么?
3. FBP算法的实现过程中需要注意哪些问题?