A Research Of Reconstruction Algorithms For Incomplete Projections Based On Compressed Sensing Theory

How to reconstruct images based on incomplete data accurately in the field of CT is anissue. Problems of incomplete data sometimes occur due to various restircitons of die body,scan geometry and radiation dose. Problems of incomplete data occur in scenairos such aslarge-size components being scanned in the ifeld of engineering as well as tooth and chestbeing scanned in clinical X-ray detection. Some serious lfaws such as low resolution andmore artifacts exist when analytical algoirthm is used to address these problems in imagereconstruciton rfom incomplete projections, whereas iterative reconstruction algorithm is ableto transform the piror information of images that need to be reconstructed into constraints oroptimal principles, creating high-quality CT images.This article is mainly about how to address the problem of reconstruction for incompleteprojection data with iterative reconstruction algorithm. The main contents include:(1)Introduce compressed sensing theory and sparse representation of images. Bycomparing wavelet transform, discrete cosine transform (DCT) and finite difference method,the study gets the conclusion that ifniet difference method is a reconstructed model by takingTotal Variation (TV) image restoration method as the objective function. This method has agood performance in restoirng contour structure of detected objects. This method is veirfiedto be feasible in the field of2D CT image reconstruction*being able to reconstruct theShepp-Lx)gan oirginal images by collecting the actual projection data in the CT imagereconstruction process.(2)Combined with compressed sensing theory, this study integrates the sparseness of CTimages into ART and improves the existing TV-ART algorithm in two aspects. Firstly, qualityand speed of images is significantly improved by introducing sequence relaxation factors, which is verified by simulation expeirments. Secondly, given the facts that conjugategradient(CG) method has fast convergence rate and TV algorithm could ensure better imageedges for the reconstructed images, the study proposes CG-TV-ART algorithm based on theintegration of conjugate gradient algoirthm and TV algorithm. There is empiircal evidenceshowing that the newly proposed algoirthm has the strengths of both the conjugate gradientalgorithm and TV algorithm, and could be able to improve the precision and speed of theimage reconstruction for incomplete projeciton data.