Super-resolution acoustic imaging using sparse recovery with spatial priming

Abstract

In this paper, we propose a new strategy to obtain superresolution maps of the sound field recorded by a spherical microphone array. In recent works, we have demonstrated that sparse recovery (SR) algorithms based on the minimisation of the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm with 0<;p≤1 can effectively produce superresolution acoustic maps. The issue with the minimisation of the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm when p<;1 is that it is a non-convex optimisation problem, thus it is likely that the algorithm converges to a local minimum. In this paper we show that we can improve the convergence of our SR acoustic imaging methods by providing, to the SR solver, priming information relating to the spatial location of the sound sources. This information can be acquired with a pre-processing, coarse analysis using standard blind source separation or direction-of-arrival techniques. Simulation results indicate that this approach can provide accurate estimates of the positions of multiple, simultaneous sound sources in the presence of noise or reverberation and even in an under-determined situation.