Fast thresholding algorithms with feedbacks for sparse signal recovery

We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various feedbacks are derived. Convergence results are also provided. The core algorithm is shown to converge in finitely many steps under a (preconditioned) restricted isometry condition. The algorithms are seen as exceedingly effective and fast, particularly for large scale problems. Numerical studies about the effectiveness and the speed of the algorithms are also presented.