编写matlab代码实现选用Shepp-Logan体模进行实验
时间: 2024-02-25 11:55:42 浏览: 22
好的,以下是基于MATLAB的Shepp-Logan体模实验代码。首先,我们需要生成Shepp-Logan体模:
```matlab
% Shepp-Logan体模参数设置
N = 256; % 图像大小
a = 1; % 长轴大小
b = 0.6; % 短轴大小
c = 0.2; % 密度
phi = [0, 0, 0, 0, 0, 0, 0]; % 旋转角度
theta = [0, pi/6, pi/3, pi/2, 2*pi/3, 5*pi/6, pi]; % 旋转方向
% 生成Shepp-Logan体模
[X,Y] = meshgrid(-1:2/(N-1):1);
m = zeros(N,N);
for i = 1:length(theta)
t = ((X*cos(theta(i))+Y*sin(theta(i))).^2)/a^2 + ((Y*cos(theta(i))-X*sin(theta(i))).^2)/b^2;
idx = t <= 1;
m(idx) = m(idx) + c*((-1)^i)*((phi(i)*pi/180)*ones(size(t(idx))));
end
```
接下来,我们将生成的Shepp-Logan体模进行投影,模拟CT扫描:
```matlab
% 投影角度设置
theta = 0:179;
% 投影得到sinogram
sinogram = radon(m, theta);
% 显示sinogram
figure;
imagesc(theta, linspace(-1, 1, size(sinogram, 1)), sinogram);
colormap(gray);
xlabel('Projection angle (degrees)');
ylabel('Projection position (normalized)');
title('Sinogram of Shepp-Logan phantom');
```
最后,我们可以将投影结果进行反投影,重建原始图像:
```matlab
% 反投影重建图像
reconstructed = iradon(sinogram, theta, 'linear', 'Ram-Lak', 1, N);
% 显示重建图像
figure;
imagesc(reconstructed);
colormap(gray);
axis square;
title('Reconstructed image of Shepp-Logan phantom');
```
完整的代码如下所示:
```matlab
% Shepp-Logan体模参数设置
N = 256; % 图像大小
a = 1; % 长轴大小
b = 0.6; % 短轴大小
c = 0.2; % 密度
phi = [0, 0, 0, 0, 0, 0, 0]; % 旋转角度
theta = [0, pi/6, pi/3, pi/2, 2*pi/3, 5*pi/6, pi]; % 旋转方向
% 生成Shepp-Logan体模
[X,Y] = meshgrid(-1:2/(N-1):1);
m = zeros(N,N);
for i = 1:length(theta)
t = ((X*cos(theta(i))+Y*sin(theta(i))).^2)/a^2 + ((Y*cos(theta(i))-X*sin(theta(i))).^2)/b^2;
idx = t <= 1;
m(idx) = m(idx) + c*((-1)^i)*((phi(i)*pi/180)*ones(size(t(idx))));
end
% 投影角度设置
theta = 0:179;
% 投影得到sinogram
sinogram = radon(m, theta);
% 显示sinogram
figure;
imagesc(theta, linspace(-1, 1, size(sinogram, 1)), sinogram);
colormap(gray);
xlabel('Projection angle (degrees)');
ylabel('Projection position (normalized)');
title('Sinogram of Shepp-Logan phantom');
% 反投影重建图像
reconstructed = iradon(sinogram, theta, 'linear', 'Ram-Lak', 1, N);
% 显示重建图像
figure;
imagesc(reconstructed);
colormap(gray);
axis square;
title('Reconstructed image of Shepp-Logan phantom');
```
希望对您有所帮助!