1. Problem description:
Computer tomography (CT) is a new non-contact non-destructive testing technology developed in the past ten years. It has high detection accuracy, reconstructed images without image overlap, spatial resolution and density resolution It has the advantages of high, direct digital processing, etc., and has been widely used in many fields such as aviation, aerospace, machinery, public security, customs, and medical treatment. The implemented algorithm is similar to the traditional filtering back-projection algorithm, but wavelet filtering is added to the algorithm, the wavelet coefficients of the image to be reconstructed are obtained after back-projection, and then these coefficients are reconstructed to obtain the local CT image. Filtered back-projection algorithm is a commonly used CT image reconstruction algorithm at present, it has fast speed and good image quality. But in the two-dimensional plane, Radon transform has no locality. Therefore, looking for a local image reconstruction algorithm that can not only reduce the radiation dose, but also reconstruct the region of interest, has aroused people's great interest. This is called local CT. Finally, MATLAB is used to simulate the filtering back projection calculation, multi-scale global reconstruction and multi-scale local reconstruction to verify the correctness of the calculation.
Reconstructing cross-sectional images of objects from projections is a very important technology in image processing. This technology can play a great role in the application of non-destructive detection of internal defects of objects. The technology of reconstructing images from projections has been made as early as the middle of the 20th century. Commodities of conventional medical diagnostic equipment. In 1917, the Austrian mathematician J. Radon published a paper that proved that two-dimensional objects or three-dimensional objects can reconstruct their internal data from many projections. The Central Research Institute of EMI in the United Kingdom designed X-ray tomography by GN Hounsfield in 1972. The analyzer was then officially named Computerized Tomography at the first international conference in Montreal, Canada in May 1974 as XCT or CT. At that time, this instrument could obtain clear and clear tomographic images of various parts of the human body. In addition, AMCormack, Tufts University in the United States in 1963 In 1991, he proposed an accurate non-iterative series expansion method for image reconstruction algorithms and pointed out the possibility of image reconstruction in diagnostic medicine. The two above were awarded the Nobel Medicine in 1979 for their pioneering contributions to the development of CT. prize.
Computer Tomography (Computed Tomography, referred to as CT) is to use a certain energy ray source (X-ray, γ-ray) to scan the object, and according to the physical quantity obtained by the detector outside the object (referring to the attenuation of the material to the ray Coefficient) the generated one-dimensional projection data, through a specific reconstruction algorithm, to obtain a two-dimensional image of the scanned tomogram.
CT tomographic images have the advantages of no image overlap, high spatial and density resolution, and direct digital processing. After more than ten years of development, they have become the mainstream technology of non-contact non-destructive testing. They are key component testing, mechanical copying design, It is a powerful means of security inspection and is widely used in aviation, aerospace, machinery, automobiles, ships, public security and other fields. In addition, in the medical field, the medical CT machine has become an important auxiliary tool for disease diagnosis, and the good reproduction of the location and extent of the lesion has made it a major medical device in the field of medical imaging.
The CT machine has three components. The first is the data acquisition system, the second is the image reconstruction (mainly the image reconstruction algorithm), and the third is the image post-processing and display system. CT image reconstruction algorithms are mainly divided into two categories, namely transformation method and series expansion method. Transformation methods include filtered back projection algorithm, Fourier transform method, rho-filtered layergrams, wavelet transform method; series expansion method is mainly algebraic reconstruction algorithm. Filtered back projection is a commonly used transformation algorithm, which has the advantages of fast speed, good spatial and density resolution.
2. Part of the program:
clc;
clear;
close all;
I=phantom(256);% production head model
figure figure(1);
imshow(I); %display image
IMG=double(I); %double precision display
[cod_a,cod_h,cod_v,cod_d,map]=wtest(IMG);% one-layer wavelet transform
figure(2);
subplot(221)
imshow(cod_a,map);
subplot(222)
imshow(cod_h,map);
subplot(223)
imshow(cod_v,map);
subplot(224)
imshow(cod_d,map);
Z1 = idwt2 (cod_a, cod_h, cod_v, cod_d, 'db1');
figure(3);
imshow(Z1,map);
for i=1:256
for j=1:256
error(i,j)=(I(i,j)-Z1(i,j))^2/I(i,j)^2;
end
end
for i=1:256
for j=1:256
if I(i,j)==0
error(i,j)=255;
end
end
end
for i=1:256
for j=1:256
if error(i,j)>255;
error(i,j)=255;
end
end
end
figure(4);
imshow(error,map);
3. Simulation conclusion:
A09-02