Research On Landweber Iterative-Filtered Back Projection Algorithm For Linear Scanning CT Image Reconstruction

Computed Tomography technology(Computed Tomography,CT)is widely used in the field of medical diagnosis,industrial inspection and safety inspection,but in practice,due to environmental constraints or short acquisition time,we cannot get the complete projection data.An incomplete projection data system is a linear scanning trajectory computed tomography(Linear Computed Tomography,LCT)system,because it uses linear scanning of the object to obtain the projection data,the scanning method is simple.However,the length of the device detector sequence in the LCT system is limited,so we can only get the projection data in the limited scanning angle range.Linear scanning trajectory CT image reconstruction is essentially a limited scan angle image reconstruction problem,therefore,it has a very important practical value to study image reconstruction algorithms for linear scanning trajectory CT.In this paper,the Landweber iterative-filtered back projection algorithm for CT scanning of linear scanning is proposed.In linear scanning trajectory CT system,the problem of reconstructing the original image from the limited angle projection data can be reduced to the problem of image reconstruction with angle-limited incomplete data,and it can be further reduced to the problem of band-limited functions extrapolation.This problem mainly focuses on Radon transform angle,and Radon transform formula is as follows:Rf(p,?)=?-?+?f(pcos?-ssin?,psin?+scos?)ds Where ? can be obtained from X-ray source angle in linear scanning system and ??(0,?/2),??[0,?/2-?)?(?/2 +?,?].For the incomplete projection data collected by linear scanning CT system,if we only use the filtered back projection image reconstruction algorithm and can not accurately reconstruct the target.In this paper,a new algorithm of image reconstruction from limited angle incomplete data based on Landweber algorithm is proposed,which is based on filtered back projection image reconstruction algorithm.Firstly,the problem of image reconstruction from limited angle incomplete data is reduced to the problem of band-limited function extrapolation.Secondly,the iterative formula of Landweber system is used to solve the problem of band-limited functions extrapolation.Meanwhile,The relaxation factor in the iterative formula of the Landweber system is studied.Through numerical simulation,it is found that the result of new algorithm is better than the filtered back projection algorithm,and when the relaxation factor ? is optimal relaxtion factor,the new algorithm has the best effect on image reconstruction.