Research On Image Reconstruction From Incomplete And Noisy Projection Data In CT

Computed Tomography (CT) is a technology that uses computer-processed x-rays toproduce tomographic images of specific areas of the scanned object, allowing the user to seewhat is inside it without cutting it open. It is widely used in medical imaging and industrialdetection. But Computed Tomography is limited by the Nyquist sampling theorem: the totalnumber of view angles must satisfy the data sufficient condition. Conventional imagereconstruction approaches, such as Filtered Back Projection (FBP), Algebraic ReconstructionTechnique (ART) and Simultaneous Algebraic Reconstruction Technique (SART), needsubstantial number of projections for a perfect reconstruction. But in some cases, theprojection data will be incomplete. Therefore, how to reduce the number of projectionswithout compromising image quality is the major problem of CT imaging. In addition, if wewant to use Computed Tomography technique to detect something in the outdoor, theprojection data will be disturbed by noise. So we need a robust algorithm. In this paper, westudy how to accurately reconstruct CT images from insufficient projection data and design arobust algorithm.In mathematics, CT image reconstruction with insufficient projection data can beexpressed as an undetermined equation problem. Because most images have sparserepresentation in transform domain, we can use Compressed Sensing theory to solve thisproblem. Compressed Sensing allows to perfectly reconstruct a signal by sampling at asignificantly smaller rate than the Nyquist rate. Inspired by its success in signal recovery, inthis paper, we propose a Compressed Sensing method to reconstruct CT images.In the noisy circumstance, the performance of Compressed Sensing method is poor, butSART method can perform well. So we propose a new method named CS-SART. It combinesCompressed Sensing and SART. CS-SART can reconstruct CT images accurately frominsufficient projection data and perform well in noisy circumstance.In this paper, we do the simulation and analysis the performance of variousreconstruction algorithms. The results show that for the insufficient projection data,Compressed Sensing method is better than conventional methods. CS-SART algorithm isrobust and can reconstruct CT images accurately.