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Optimization of Fan-beam Convolution Back Projection Algorithm

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Computed Tomography technique(CT) has become a new nondestruc-tive detection method in recent years,It utilizes the mutual physical characteristic of object material and ray and the operation ability of the computer, to through projection data of several direction that the cross section of object , it get physics characteristic of object cross-section to perform instead through special algorithm; which is of good quality and high resolution。It can be processed and analyzed digitally, so it is applied widely in aviation, shipping, automobile, public security, medical and other areas。CT machine has three components。First, system of data collecting, second, image reconstruction(mainly, algorithms of image reconstruction), third,the aftertreatment of the image and display system。CT image reconstruction algorithm has two categories, namely algorithm of progression spread and transform。The former dispersed to take image at the beginning, it show into a group of unknown variables of the equation group, and then to solve it through the algebraic method;The latter, the analytic vary at continuous land first, to get Radon inverse transformation of the imminent expression formul of different forms, and to calculate dispersedly it again。Back projection algorithm (have another name called the total method) being easier to realize, basic principle of it to get every any have examined and got projection value according to original route average distribution their (call backprojection), all directions projection superpose in the image after back projection, thus infer out the original image of。But,it get the ropy image Back projection algorithm,it has astroid false mark and exist fuzzy and anamorphic。To against the shortcoming of backprojection algorithm, it bring the filtered Back projection algorithm, widely used of CT <WP=59>technology, because this algorithm has given consideration to time and quality of reconstruction。 It has a little calculationalquantity and fast reconstruction speed, the reconstructed image has very fine resolution ratio of space and density。The algorithm diagram is following: Back projection reconstruction is the integral operation,fi-lter is the Convolution operation, both are the linear operation, The operation order can be exchanged。the Back projection in the front and the filter in after called filtered Back projection, contrarily called Convolution Back projection。Convolution Back projection algorithm for dispel image fuzzy , it adopt proper right function to filter, to make the original data to distortion, then Back projection , its diagram is following:Convolution Back projection algorithm the same as filtered Back projection algorithm in hypostasis the difference the former filter in special area, the latter in frequency area, so the former do not carry on the Fourier transform , it has a fast speed , has a better reconstruction quality of image。This text adopts the convolution Back projection algorithm。Image reconstruction by Convolution Back projection algorithm, first ,to make initial data that get at detection and Convolution function to convolution operation ,get the projection function of the convolution of every direction, and Back projection , get every matrix CT value of yuan from every direction them according to original route average allocation its to go on; Can is it scan into fault image of object to get after deal with properly and then, convolution can dispel losing the sharp effect against projection against the edge producing in projection <WP=60>simple, high-frequency composition to compensate projection and reduce projection centre density , is it reconstruction image edge clarity and inside distribute evenly to guarantee. Though Convolution Back projection algorithm compare with other image reconstruction algorithm , it has have higher operation efficiency, but, because the data of CT is very huge, the calculation of the image reconstruction consumed more time, foreign CT adopt based on 64 CPUs work station and collocate the arry d


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