Robust regularized tomographic imaging with convex projections

A robust method for tomographic image reconstruction from limited-angle noisy measurements is proposed which builds upon a combination of regularization theory and the method of projections onto convex sets (POCS). Two specific formulations of the proposed method, namely, Tikhonov-POCS and TV-POCS, are introduced and investigated. A statistical framework is developed that provides insight into the behavior of the two algorithms. The inclusion of a reference image is approached by either a coarse reconstruction or a model generated background image. The method is validated in the context of simulations for the reconstruction of highly structured images from partial projections. Results demonstrate significant improvement over conventional regularization methods in situations where the conventional techniques are inadequate.