Research On CT Image Reconstruction From Sparse-View Projections Via Fourier Iterative Methods

Over the past several decades,under the condition of non-contact and non-destructibility,Computed Tomography(CT)has been widely used in medical diagnosis,security check,industrial nondestructive testing and other fields,which acquires inner structure information with high precision for scanned object.The sparse scanning manner of CT system not only speeds up imaging and decreases the amount of projection,but also reduces radiation dose and hardware cost of each scanning.CT reconstruction from sparse view is an ill-posed problem due to only few projections.Therefore,the research on rapid and efficient reconstruction algorithm is one of the hottest spot and of significant value in both theoretical and practical aspects.At present,the general method for sparse view is iterative reconstruction algorithm which based on sparse optimization theory in the spatial domain.This spatial iterative algorithm can efficiently overcome the influence of artifacts and noise while face with inevitable shortcoming of computation resource and reconstruction rate.Based on the central slice theory,Fourier-based iterative reconstruction technique,which depends on the advantages of computation time and memory allocation by Fast Fourier Transform(FFT),greatly improve the reconstruction performance.Considering the foundation of sparse optimization theory,this dissertation focuses on the Fourier-based iterative reconstruction algorithm from sparse views for parallel-beam and fan-beam CT,respectively.The main work is included as follows:1.Although the iterative next neighbor gridding(INNG)reveals remarkable performance for parallel-beam CT with full projection,it is easily suffer from streaking artifacts when deal with sparse view reconstruction.Aiming at this problem,an iterative next neighbor gridding algorithm combined with total variation(TV)gradient descent method(INNG-TV)is presented.The algorithm is based on INNG and utilizes TV regularization which comes from piecewise constant of CT image characterization,and the reconstruction goal of sparse view is realized.Experimental results indicate that compared with direct INNG algorithm,INNG-TV algorithm can improve image quality by restraining streaking artifacts;compared with spatial iterative method,the proposed algorithm can speed up reconstruction with improving the reconstruction quality.2.The data distribution of spatial and Fourier domain for FFT is evenly distributed and strictly limited to Cartesian coordinate.However,the Fourier data,which come from one-dimensional FFT of parallel-beam projections,is non-uniformly distributed at polar coordinate.Meanwhile,the interpolation error will be introduced due to the transformation form polar to Cartesian coordinate.According to the capacity for dealing with non-uniform spaced data of Non-Uniform Fast Fourier Transform(NUFFT),a Fourier-based iterative reconstruction technique is developed in conjunction with advanced TV minimization,which converts sparse view reconstruction problem to constrained TV minimization by sparse optimization theory and alternating direction method(ADM)scheme is used to solve the problem.Simulation and real data reconstruction experiments demonstrate that compared with the existing spatial TV minimization techniques,the proposed algorithm has characteristic of low computational complexity and short reconstruction time and outperform in term of reconstruction quality under same iterative time.3.Since there is no correspondence spatial frequency relation in fan-beam CT,the sparse view fan-beam projection needs rebin to parallel-beam projection.According to the geometric relation between fan-beam and parallel-beam,the parallel projection data after rebinning for sparse fan-beam projection is incomplete in every angle.Aim at this phenomenon,the paper introduces selective matrix to recorder the location of the value after rebinning,then designs TV minimization model for Fourier-based iterative reconstruction which is solved by ADM by reformulating into two sub-problems with analytic solution.Experimental results show that the presented Fourier-based algorithm is not only have characteristic of high computational efficiency and low memory allocation,but also gain high precise reconstruction image for sparse fan-beam projection.