Radon变换的matlab实现

1、§ 5.4 Radon变换5.4.4 Matlab 中的实现 4例、对一个正方形黑框进行 Radon 变换。I=zeros(200,200);I(100:170,100:170)=1;% to produce a square black frameFigure,imshow(I) ；title('origine image') ； to do Radon transform of 0 and 25 degreeR,xp=radon(I,0 25);% to calculate the Radon transform of the black frame，% R sh

2、ows the Radon transform values for theta angles: % 0 and 25 degree;% xp矢量表示沿？'轴相应的坐标值subplot(1,3,2),plot(xp,R(:,1);title('R(OS)(xprime)');subplot(1,3,3),plot(xp,R(:,2);title('R(25Ao)(xprime)');origins image-200 0 20080706050403D20100200 0 200% to do Radon tran sform from 0 degree

3、 to 180 degreetheta=0:180;% to define an an gular vector from 0 to 180 degreeR,xp=radon(l,theta); % to calculate Radon Transform from 0 to 180figure, imagesc(theta,xp,R);% IMAGESC(.) is the same as IMAGE(.) except the data is % scaled to use the full colormap 也就是说，imagesc能自动 %调整值域范围title('R_thet

4、a(Xprime)');xlabel('theta(degree)');ylabel('X'prime');set(gca,'Xtick',0:20:180);% to set the properties of axiscolormap(hot);2colorbar; %显示颜色条，将图像中使用的色彩排列在图像旁边-100-5D050100020406080100120140160180©(degree)908070GO4030203#MATLAB中的逆Radon变换函数，是利用滤波后向投影算法来 计算逆变换R=ira

5、do n( R,theta)其中R=radon(l,theta)是图像I的Radon变换：1) 在求逆变换时，利用R各列中的投影来构造图像I的近似值；2) 使用的投影数越多，所获得的图像越接近原始图像；3) theta矢量必须是固定增量的均匀矩阵，即每次角度增加值为常数，若角度增加值已知，可以作为参数取代theta值传入 iradon 函数;4）投影值含有噪声时，可以通过加窗消去高频噪声：IR=iradon(R,theta,'Shepp-Logan');% 采用 Shepp-Logan 窗做滤波： The Shepp-Logan filter multiplies% the R

6、am-Lak filter by a sinc function.IR=iradon(R,theta,' Cosine');% 采用 Cosine 窗做滤波： The cosine filter multiplies the Ram-Lak% filter by a cosine function.IR=iradon(R,theta, 'Hamming');% 采用 Hamming 窗做滤波： The Hamming filter multiplies the% Ram-Lak filter by a Hamming window.IR=iradon(R,the

7、ta,0.90);% iradon 允许指定归一化频率 D ，高于 D 的滤波器响应为零，整 % 个滤波器压缩在 0,D 的范围内。假若系统不含高频信息而存在 % 高频噪声时可用来完全拟制噪声，又不会影响图像重建。例、从一个简单图像的投影重建图像在 Matlab 图像处理工具箱中的 Phantom 函数，可以产生 Shepp Logan 的大脑图， 该图作为一个测试图， 可反映人大脑的许多性质。P=phantom(256);% P = PHANTOM(DEF,N) generates an image of a head phantom that can % be usedto test th

8、e numerical accuracy of RADON and IRADON or other % 2-D reconstruction algorithms. P is a grayscaleintensity image that % consists of one large ellipse (representing the brain) containing % several smaller ellipses (representingfeatures in the brain). figure,imshow(P);title('image of a head phan

9、tom of Shepp-Logg');theta1=0:10:170;R1,xp=radon(P,theta1);% to calculate radon transform of R1 which includes 18 angles theta2=0:5:175;R2,xp=radon(P,theta2);% to calculate radon transform of R2 which includes 36 angles theta3=0:2:178;R3,xp=radon(P,theta3);% to calculate radon transform of R3 whi

10、ch includes 90 angles figure,imagesc(theta1,xp,R1);% IMAGESC(.) is the same as IMAGE(.) except the data is% scaled to usethe full colormap.title('R_theta(Xprime)'); title('radon transform of 18 angles for Shepp-logan head phanto '); xlabel('theta(degree)');ylabel('Xprime&

11、#39;); set(gca,'Xtick',0:20:180); % to set the properties of axis colormap(hot);colorbar;figure, imagesc(theta2,xp,R2); title('radon transform of 36 angles for Shepp-logan head phanto'); xlabel('theta(degree)');ylabel('Xprime');set(gca,'Xtick',0:20:180);% to s

12、et the properties of axiscolormap(hot);colorbar;figure, imagesc(theta3,xp,R3);title('radon transform of 90 angles for Shepp-logan head phanton'); xlabel('theta(degree)');ylabel('Xprime');set(gca,'Xtick',0:20:180);% to set the properties of axiscolormap(hot);colorbar;I

13、R1=iradon(R1,theta1,0.85); % 指定归一化频率为 0。 85 figure,imshow(IR1);title('reconstruction for radon transform of 18 angles');IR2=iradon(R2,theta2,0.85);figure,imshow(IR2);title('reconstruction for radon transform of 36 angles');IR3=iradon(R3,theta3,0.85);figure,imshow(IR3);title('rec on structi on for radon tran sform of 90 an gles');7#image of a head phantom nf Shepp-Logg#radon transform of 18 angles for Shepp-logan head pharito02040 BO 80100120140160©(degree)-60-505这个图的外部椭圆形是头骨，内部的椭圆形是大脑的内部特征或者是肿瘤。150100-50050100150#adon transf