Efficient TpV minimization for circular, cone-beam computed tomography reconstruction via non-convex optimization

An efficient iterative algorithm, based on recent work in non-convex optimization and generalized p-shrinkage mappings, is proposed for volume image reconstruction from circular cone-beam scans. Conventional total variation regularization makes use of L1 norm of gradient magnitude images (GMI). However, this paper utilizes a generalized penalty function, induced by p-shrinkage, of GMI which is proven to be a better measurement of its sparsity. The reconstruction model is formed using generalized total p-variation (TpV) minimization, which differs with the state of the art methods, with the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. Theoretically, the proximal mapping for penalty functions induced by p-shrinkage has an exact and closed-form expression; thus, the constrained optimization can be stably and efficiently solved by the alternating direction minimization (ADM) scheme. Each sub-problem decoupled by variable splitting is minimized by explicit and easy-to-implement formulas developed by ADM. The proposed algorithm is efficiently implemented using a graphics processing unit and is referred to as "TpV-ADM." This method is robust and accurate even for very few view reconstruction datasets. Verifications and comparisons performed using various datasets (including ideal, noisy, and real projections) illustrate that the proposed method is effective and promising.