Compressed signal reconstruction using the correntropy induced metric

Recovering a sparse signal from insufficient number of measurements has become a popular area of research under the name of compressed sensing or compressive sampling. The reconstruction algorithm of compressed sensing tries to find the sparsest vector (minimum l_o-norm) satisfying a series of linear constraints. However, l_o-norm minimization, being a NP hard problem is replaced by l_i-norm minimization with the cost of higher number of measurements in the sampling process. In this paper we propose to minimize an approximation of l_o-norm to reduce the required number of measurements. We use the recently introduced correntropy induced metric (CIM) as an approximation of l_o-norm, which is also a novel application of CIM. We show that by reducing the kernel size appropriately we can approximate the l_o-norm, theoretically, with arbitary accuracy.