在MATLAB中从正弦图中获取投影

Question

我正在进行X射线断层扫描图像重建，并尝试使用其正弦图在MATLAB中重建图像，但它没有正常工作。在这里你可以找到我用过的代码。第一部分用于计算效果良好的正弦图。第二部分（从写入％backprojection的行开始）用于计算反投影（没有任何滤波器），问题出在这一部分。重建的图像不正确。任何人都可以帮我编写代码或向我介绍另一个计算反投影的代码吗？顺便说一句，我不想​​使用MATLAB内置代码，例如 radon 或 iradon 。

clc
clear all
I=phantom('Modified Shepp-Logan',600);
[N,M]=size(I);
% center of the image
m=round(M/2);
n=round(N/2);
% total number of rhos = number of pixels on the diagonal
rhomax=ceil(sqrt(M^2+N^2));
rc=round(rhomax/2);
%matrix to store the results
res=cast(zeros(rhomax+1,180),'double');
tic
for t=1:45 % below 45 degree use y as variable
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta; % y=ax+b
    for r=1:rhomax
        rho=r-rc;
        b=rho/sintheta; % y=ax+b
        ymax=min(round(-a*m+b),n-1);
        ymin=max(round(a*m+b),-n);
        for y=ymin:ymax
            x=(y-b)/a;
            xfloor=floor(x); % the integer part of x
            xup=x-xfloor; % the decimal of x
            xlow=1-xup;
            x=xfloor;
            x=max(x,-m);
            x=min(x,m-2);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+xlow*I(y+n+1,x+m+1);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+xup*I(y+n+1,x+m+2);
        end
    end
end
for t=46:90
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta; % y=ax+b
    for r=1:rhomax 
        rho=r-rc;
        b=rho/sintheta; % y=ax+b
        xmax=min(round((-n-b)/a),m-1);
        xmin=max(round((n-b)/a),-m);
        for x=xmin:xmax
            y=a*x+b;
            yfloor=floor(y);
            yup=y-yfloor;
            ylow=1-yup;
            y=yfloor;
            y=max(y,-n);
            y=min(y,n-2);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+ylow*I(y+n+1,x+m+1);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+yup*I(y+n+2,x+m+1);
        end
    end
end
for t=91:135
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta;
    for r=1:rhomax
        rho=r-rc;
        b=rho/sintheta;
        xmax=min(round((n-b)/a),m-1);
        xmin=max(round((-n-b)/a),-m);
        for x=xmin:xmax
            y=a*x+b;
            yfloor=floor(y);
            yup=y-yfloor;
            ylow=1-yup;
            y=yfloor;
            y=max(y,-n);
            y=min(y,n-2);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+ylow*I(y+n+1,x+m+1);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+yup*I(y+n+2,x+m+1);
        end
    end
end
for t=136:179
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta; % y=ax+b
    for r=1:rhomax 
        rho=r-rc;
        b=rho/sintheta;
        ymax=min(round(a*m+b),n-1);
        ymin=max(round(-a*m+b),-n);
        for y=ymin:ymax
            x=(y-b)/a;
            xfloor=floor(x); % the integer part of x
            xup=x-xfloor; % the decimal of x
            xlow=1-xup;
            x=xfloor;
            x=max(x,-m);
            x=min(x,m-2);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+xlow*I(y+n+1,x+m+1);
            res(rhomax-r+1,180-t)=res(rhomax-r+1,180-t)+xup*I(y+n+1,x+m+2);
        end
    end
end
for t=180
    rhooffset=round((rhomax-M)/2);
    for x=1:M
        r=x+rhooffset;
        r=rhomax-r+1;
        for y=1:N
            res(r,t)=res(r,t)+I(y,x);
        end
    end
end
toc
rhoaxis=(1:rhomax+1)-rc;
figure
imshow(res,[]);
%backprojection
res1=cast(zeros(600),'double');
[N1,M1]=size(res1);
m1=round(M1/2);
n1=round(N1/2);
rhomax1=ceil(sqrt(m1^2+n1^2));
rc1=round(rhomax1/2);
tic
for t=1:45 % below 45 degree use y as variable
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta; % y=ax+b
    for r=1:rhomax1
        rho=r-rc1;
        b=rho/sintheta; % y=ax+b
        ymax=min(round(-a*m1+b),n1-1);
        ymin=max(round(a*m1+b),-n1);
        for y=ymin:ymax
            x=(y-b)/a;
            xfloor=floor(x); % the integer part of x
            xup=x-xfloor; % the decimal of x
            xlow=1-xup;
            x=xfloor;
            x=max(x,-m1);
            x=min(x,m1-2);
            res1(y+n1+1,x+m1+1)=res1(y+n1+1,x+m1+1)+res(rhomax1-r+1,t);
        end
    end
end
for t=46:90
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta; % y=ax+b
    for r=1:rhomax1 
        rho=r-rc1;
        b=rho/sintheta; % y=ax+b
        xmax=min(round((-n1-b)/a),m1-1);
        xmin=max(round((n1-b)/a),-m1);
        for x=xmin:xmax
            y=a*x+b;
            yfloor=floor(y);
            yup=y-yfloor;
            ylow=1-yup;
            y=yfloor;
            y=max(y,-n1);
            y=min(y,n1-2);
            res1(y+n1+1,x+m1+1)=res1(y+n1+1,x+m1+1)+res(rhomax1-r+1,t);
        end
    end
end 
for t=91:135
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta;
    for r=1:rhomax1
        rho=r-rc1;
        b=rho/sintheta;
        xmax=min(round((n1-b)/a),m1-1);
        xmin=max(round((-n1-b)/a),-m1);
        for x=xmin:xmax
            y=a*x+b;
            yfloor=floor(y);
            yup=y-yfloor;
            ylow=1-yup;
            y=yfloor;
            y=max(y,-n1);
            y=min(y,n1-2);
            res1(y+n1+1,x+m1+1)=res1(y+n1+1,x+m1+1)+res(rhomax1-r+1,t);
        end
    end
end
for t=136:179
    costheta=cos(t*pi/180);
    sintheta=sin(t*pi/180);
    a=-costheta/sintheta; % y=ax+b
    for r=1:rhomax1 
        rho=r-rc1;
        b=rho/sintheta;
        ymax=min(round(a*m1+b),n1-1);
        ymin=max(round(-a*m1+b),-n1);
        for y=ymin:ymax
            x=(y-b)/a;
            xfloor=floor(x); % the integer part of x
            xup=x-xfloor; % the decimal of x
            xlow=1-xup;
            x=xfloor;
            x=max(x,-m1);
            x=min(x,m1-2);
            res1(y+n1+1,x+m1+1)=res1(y+n1+1,x+m1+1)+res(rhomax1-r+1,t);
        end
    end
end
toc
rhoaxis1=(1:rhomax1+1)-rc1;
res1=res1./90;
figure
imshow(res1,[]);