Minimum Trace Norm Regularization (MTNR) in Electromagnetic Inverse Problems

This paper discusses a method to regularize linear problems in presence of incomplete and noisy data generated by partially or totally unknown sources. The idea is to identify the “simplest” solution, looking for the system having the minimum number of degrees of freedom (NDF) compatible with the available data. It is shown that a normalized version of the trace norm (known as 1-Schatten norm in functional analysis) is a good convex approximation of the NDF of the field. This allows to use the trace norm as a convex surrogate of the NDF in the minimization process, taking advantage of the recent literature on rank minimization. Examples regarding MIMO beamforming from incomplete channel matrix, field interpolation with no a priori information on the sources, and land-mine identification using the total field are discussed.