使用RL,SL,Hamming，Hanning，Cosine滤波函数的滤波反投影重建图像的matlab代码

由于没有提供具体的数据集和重建算法，以下代码仅提供基本的滤波函数实现：

1. RL滤波函数：

function h = RL_filter(N, d0, a)
% N: filter size
% d0: cutoff frequency
% a: parameter

    h = zeros(N,1);
    for i = 1:N
        u = (i - N/2 - 1)/(N/2);
        if abs(u) <= d0/a
            h(i) = 1;
        elseif abs(u) > d0/a && abs(u) <= d0
            h(i) = 0.5 * (1 + cos(pi*a*(abs(u)-d0/a)/(d0-d0/a)));
        else
            h(i) = 0;
        end
    end
end

2. SL滤波函数：

function h = SL_filter(N, d0, a)
% N: filter size
% d0: cutoff frequency
% a: parameter

    h = zeros(N,1);
    for i = 1:N
        u = (i - N/2 - 1)/(N/2);
        if abs(u) <= d0/a
            h(i) = 1;
        elseif abs(u) > d0/a && abs(u) <= d0
            h(i) = (d0 - abs(u))/(d0 - d0/a);
        else
            h(i) = 0;
        end
    end
end

3. Hamming窗函数：

function w = Hamming_window(N, alpha)
% N: window size
% alpha: parameter

    w = zeros(N,1);
    for i = 1:N
        w(i) = alpha - (1-alpha)*cos((2*pi*(i-1))/(N-1));
    end
end

4. Hanning窗函数：

function w = Hanning_window(N)
% N: window size

    w = zeros(N,1);
    for i = 1:N
        w(i) = 0.5 - 0.5*cos((2*pi*(i-1))/(N-1));
    end
end

5. Cosine窗函数：

function w = Cosine_window(N)
% N: window size

    w = zeros(N,1);
    for i = 1:N
        w(i) = sin((pi*(i-0.5))/N);
    end
end

6. 滤波反投影重建代码：

function img = FBPR_reconstruction(proj, theta, N, d, filter, window)
% proj: projection data (N x n_theta)
% theta: projection angles (n_theta x 1)
% N: image size (N x N)
% d: pixel size
% filter: filter function (handle)
% window: window function (N x N)

    n_theta = length(theta);
    img = zeros(N,N);

    for i = 1:n_theta
        % filtering
        proj(:,i) = filter_projection(proj(:,i), filter, N, d);
        % backprojection
        img = img + backprojection(proj(:,i), theta(i), N, d);
    end

    % windowing
    img = img .* window;

    % normalization
    img = img / (pi*n_theta/2);

end

function proj_f = filter_projection(proj, filter, N, d)
% proj: projection data
% filter: filter function (handle)
% N: image size (N x N)
% d: pixel size

    % FFT
    proj_f = fft(proj);

    % frequency axis
    freq = (-N/2:N/2-1)/(N*d);

    % filtering
    filter_f = filter(N, freq);
    proj_f = proj_f .* filter_f.';

    % inverse FFT
    proj_f = ifft(proj_f);

end

function img_bp = backprojection(proj, theta, N, d)
% proj: projection data
% theta: projection angle
% N: image size (N x N)
% d: pixel size

    img_bp = zeros(N,N);

    % coordinates of image center
    xc = (N+1)/2;
    yc = (N+1)/2;

    % coordinates of image pixels
    [x,y] = meshgrid(1:N,1:N);
    x = (x - xc)*d;
    y = (y - yc)*d;

    % backprojection
    for i = 1:length(proj)
        t = theta(i);
        p = proj(i);
        img_bp = img_bp + p * interp1([cos(t-pi/2),cos(t+pi/2)],[x(:),y(:)],cos(t)*x(:)+sin(t)*y(:),'linear',0);
    end

end