Radon變換的matlab實現(xiàn)

1、§ 5.4 Radon變換5.4.4 Matlab 中的實現(xiàn) 4例、對一個正方形黑框進行 Radon 變換。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？'軸相應的坐標值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 也就是說，imagesc能自動 %調(diào)整值域范圍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; %顯示顏色條，將圖像中使用的色彩排列在圖像旁邊-100-5D050100020406080100120140160180©(degree)908070GO4030203#MATLAB中的逆Radon變換函數(shù)，是利用濾波后向投影算法來 計算逆變換R=ira

5、do n( R,theta)其中R=radon(l,theta)是圖像I的Radon變換：1) 在求逆變換時，利用R各列中的投影來構造圖像I的近似值；2) 使用的投影數(shù)越多，所獲得的圖像越接近原始圖像；3) theta矢量必須是固定增量的均勻矩陣，即每次角度增加值為常數(shù)，若角度增加值已知，可以作為參數(shù)取代theta值傳入 iradon 函數(shù);4）投影值含有噪聲時，可以通過加窗消去高頻噪聲：IR=iradon(R,theta,'Shepp-Logan');% 采用 Shepp-Logan 窗做濾波： The Shepp-Logan filter multiplies% the R

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

7、ta,0.90);% iradon 允許指定歸一化頻率 D ，高于 D 的濾波器響應為零，整 % 個濾波器壓縮在 0,D 的范圍內(nèi)。假若系統(tǒng)不含高頻信息而存在 % 高頻噪聲時可用來完全擬制噪聲，又不會影響圖像重建。例、從一個簡單圖像的投影重建圖像在 Matlab 圖像處理工具箱中的 Phantom 函數(shù)，可以產(chǎn)生 Shepp Logan 的大腦圖， 該圖作為一個測試圖， 可反映人大腦的許多性質。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); % 指定歸一化頻率為 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這個圖的外部橢圓形是頭骨，內(nèi)部的橢圓形是大腦的內(nèi)部特征或者是腫瘤。150100-50050100150#adon transf