An Improved Weighted Total Variation Algorithm for Compressive Sensing

In this paper, we present a new algorithm to achieve faster signal reconstruction with higher quality from fewer measurements compared to the classical l(1)-based minimization approach. Specifically, for a given noisy signal, firstly, the algorithm detects an index set I that includes components most likely to be a jump and increases over the iterations before all jumps have been detected to update the weights. Secondly, the algorithm for the minimization problem updates all the components of signal according to the weights. We analyze this algorithm, and compare its numerical performance with total variation (TV) algorithm and basis pursuit (BP) algorithm. Our numerical simulations on recovering 1D signal indicate that the proposed algorithm has significant advantages over the classical l(1)-based minimization approach.