Sampling conditions for gradient-magnitude sparsity based image reconstruction algorithms

We seek to characterize the sampling conditions for iterative image reconstruction exploiting gradient-magnitude sparsity. We seek the number of views necessary for accurate image reconstruction by constrained, total variation (TV) minimization, which is the optimization problem suggested in the compressive sensing (CS) community for this type of sparsity. The preliminary finding here, based on simulations using images of realistic sparsity levels, is that necessary sampling can go as low as N/4 views for an NxN pixel array. This work sets the stage for fixed-exposure studies where the number of projections is balanced against the X-ray intensity per projection.