A new algorithm for compressive sensing based on total-variation norm

A new algorithm for the reconstruction of images with sparse gradient is proposed. The algorithm is based on the minimization of the so called total-variation (TV) regularized squared error and is especially suited for image reconstruction from a small number of measurements. The algorithm is developed based on a generalized TV norm and uses a sequential conjugate-gradient method. Simulation results are presented which demonstrate that the proposed algorithm yields significantly improved reconstruction performance for images with sparse gradient and requires significantly reduced computational effort relative to the log-barrier based TV-regularized least-squares algorithm.