An Accelerated Total-Variation Compressive Sensing Approach to Field Strength Reconstruction

Abstract

An innovative and computationally efficient compressive sensing (CS) inversion scheme is proposed for the prediction of the 2-D distribution of the electromagnetic (EM) field strength (FS) in a region of interest (RoI) starting from a limited set of FS measurements, but without any information on the EM radiating source. Toward this end, the inverse problem at hand is recast to the minimization of the augmented Lagrangian function, and then it is efficiently solved by means of a novel accelerated total-variation CS (ATV-CS) approach. The ATV-CS, which is based on a smart implementation of the involved matrix–vector multiplications, is exploited to remarkably reduce the computational cost of the standard total variation (TV)-CS so that a reliable and efficient prediction of the FS is enabled in realistic applications concerned with wide areas, as well. A set of representative test cases, from a wide numerical assessment concerned with different sources and propagation scenarios, is reported to assess both the reliability/effectiveness and the computational efficiency of the proposed approach in comparison with competitive state-of-the-art sparseness-promoting techniques, as well.