Nonconvex optimization for improved exploitation of gradient sparsity in CT image reconstruction

A nonconvex optimization algorithm is developed, which exploits gradient magnitude image (GMI) sparsity for reduction in the projection view angle sampling rate. The algorithm shows greater potential for exploiting GMI sparsity than can be obtained by convex total variation (TV) based optimization. The nonconvex algorithm is demonstrated in simulation with ideal, noiseless data for a 2D fan-beam computed tomography (CT) configuration, and with noisy data for a 3D circular cone-beam CT configuration.