Full Sequential Projection Onto Convex Sets For CT Reconstruction

The birth of Computed Tomography(CT)is of epoch-making significance for medical diagnosis.In CT,it is sometimes necessary to reduce x-ray exposure for patient health,particularly for brain tissue,so we need limited-angle projection data.Therefore,the problem of image reconstruction with limited angle projection data has become hot topic among scholars.Since the gradient image of the original image is generally sparse,total variation(TV)regularization is often used in CT image reconstruction for limited angle projection data,such as total-variation projection onto convex set(TV-POCS)image reconstruction algorithm.It's iterative process includes two major steps: projection onto convex sets(POCS)for the convex constraint and gradient descent on the TV function.This two-step algorithm greatly improves the efficiency of image reconstruction.But the Lagrange parameter for balancing data fidelity and the TV minimization regularization and the step size of the gradient descent process for the TV regularization are dependent on empirical selection and can't be uniformly applied to the reconstruction of projection data of different types,which will greatly affect the property of reconstruction images and reconstruction efficiency.To solve this problem,a new reconstruction framework is proposed in this paper,in which the TV minimization function is transformed into convex set,and based on the alternating projection method,using POCS to find the solution in the intersection of convex constraints of bounded TV function,bounded data fidelity error and non-negativity,i.e.true image.The TV minimization part is transformed into a convex set,which is the TV minimization's relaxed form,and using this relaxed form to project can make the algorithm have faster convergence speed.As the classical regularization constraint,the greatest advantage of TV regularization is that it can effectively retain the edge information of the image.The PES-TV algorithm is used to project onto TV convex set.The projection process does not need to estimate the parameters to reconstruct the great results.In this paper,a full sequential alternating projections or POCS(FS-POCS)algorithm is proposed based on this reconstruction framework.The calculationprocess is similar to the TV-POCS algorithm.However,unlike the TV-POCS algorithm,the objective function which needs to be solved is deduced and the PDHG algorithm is used to solve the convex set of bounded TV function.In addition,the parameters of TV-POCS algorithm need to be selected empirically,so we also deduced the convergence conditions of the gradient descent process and the parameters need to meet the conditions for convergence.The original TV-POCS algorithm may not find the optimal solution,but based on the POCS theory,this paper ensures that it can converge to a point near the original optimal solution,which is closest to the start point in the intersection of the three relaxed sets.