shepp-logan模型笛卡爾座標變換到極座標，環狀僞影仿真

利用shepp-logan模型進行環狀僞影仿真，處理方法爲後處理方法，即對CT圖像進行處理，將圖像從笛卡爾座標變換到極座標系中。

clc
clear all
L = 256;**圖像大小
P = phantom(L);
theta = 0:359;
R = radon(P,theta);**獲得正弦圖
for ii = 200:200
    for jj = 1:360
        R(ii,jj) = 0.0;
    end
end
for ii = 100:100
    for jj = 1:360
        R(ii,jj) = 0.0;
    end
end
for ii = 150:150
    for jj = 1:360
        R(ii,jj) = 0.0;
    end
end
%figure,imshow(R,[])
I = iradon(R, theta, 'linear', 'Hamming', L);%%獲得重建圖像
JG = 2*pi/(4*L);%%角度採樣頻率
width = 2*pi/(JG) + 1;
[m,n] = size(I);
radius = ceil(sqrt(m^2 + n^2)/2);
POL = zeros(radius*2, width);
for gama = 0:JG:(2*pi)
    for rad = 0.25:0.25:radius   %%半徑採樣頻率
        i = round(gama/JG+1);
        j = (rad-0.25)*4 + 1;
        x = rad*cos(gama);%%x座標變換
        y = rad*sin(gama);%%y座標變換
        ceil_x = ceil(x);
        ceil_y = ceil(y);
        floor_x = floor(x);
        floor_y = floor(y);
        chae3 = abs(x - floor_x);
        chae4 = abs(y - floor_y);
        x1 = floor_x + L/2;
        x2 = ceil_x + L/2;
        y1 = floor_y + L/2;
        y2 = ceil_y + L/2;
        if x1>L
            x1 = L;
        end
        if x1<1
            x1 = 1;
        end
        if x2>L
            x2 = L;
        end
        if x2<1
            x2 = 1;
        end
        if y1>L
            y1 = L;
        end
        if y1<1
            y1 = 1;
        end
        if y2>L
            y2 = L;
        end
        if y2<1
            y2 = 1;
        end
        POL(j,i) = (1-chae3)*(1-chae4)*I(x1,y1) + chae3*(1-chae4)*I(x2,y1) + (1-chae3)*chae4*I(x1,y2) + chae3*chae4*I(x2,y2);%%雙線性插值
    end
end
figure, hold on
subplot(1,2,1),imshow(I)
subplot(1,2,2),imshow(POL)

結果如下圖所示