matlab fbp代码

以下是一个简单的Matlab FBP代码示例：

function [image] = fbp(sinogram,angles,filter_type)
% FBP function to reconstruct an image from a sinogram
%
% INPUTS:
% sinogram - a 2D array representing the sinogram
% angles - a 1D array of projection angles (in degrees)
% filter_type - a string specifying the filter type ('ram-lak', 'shepp-logan', 'cosine', 'hamming')
%
% OUTPUT:
% image - the reconstructed image

% Step 1: Set up the filter
num_angles = length(angles);
num_detectors = size(sinogram,1);
theta = linspace(0,180,num_angles+1);
theta = theta(1:end-1);

% Create the filter
switch filter_type
    case 'ram-lak'
        filter = abs(linspace(-1,1,num_detectors));
    case 'shepp-logan'
        filter = shepp_logan_filter(num_detectors);
    case 'cosine'
        filter = cos(linspace(0,pi,num_detectors));
    case 'hamming'
        filter = hamming(num_detectors);
    otherwise
        error('Filter type not recognized');
end

% Step 2: Compute the backprojection
backprojection = zeros(num_detectors,num_detectors);
for i = 1:num_angles
    projection = sinogram(i,:);
    filtered_projection = ifft(filter.*fft(projection));
    backprojection = backprojection + interp1(linspace(-1,1,num_detectors),filtered_projection,theta(i)+linspace(-1,1,num_detectors),'linear',0);
end
backprojection = backprojection./num_angles;

% Step 3: Apply the ramp filter
ramp_filter = abs(linspace(-1,1,num_detectors));
filtered_backprojection = ifft(ramp_filter.*fft(backprojection));

% Step 4: Convert to image space
image = iradon(filtered_backprojection,angles,'linear','Ram-Lak',1,num_detectors);
end

% Function to create the Shepp-Logan filter
function [filter] = shepp_logan_filter(num_detectors)
filter = zeros(1,num_detectors);
for i = 1:num_detectors
    if i <= num_detectors/2
        filter(i) = abs(i-num_detectors/2)/(num_detectors/2);
    else
        filter(i) = abs(i-num_detectors/2)/(num_detectors/2);
    end
end
end

这个函数需要三个输入参数：sinogram（一个2D数组表示的投影数据），angles（一个1D数组表示的投影角度），filter_type（一个字符串，指定使用哪种滤波器）。

该函数的输出是重建图像。

在该函数中，首先根据所选的滤波器类型创建一个滤波器。然后，通过对每个角度的投影数据进行滤波和反投影来计算反投影。最后，使用斜坡滤波器将反投影滤波，并将其转换为图像空间。

注意，该代码示例中使用的是Matlab的`iradon`函数进行反投影。在一些情况下，可能需要使用其他反投影算法。