Multichannel myopic deconvolution in underwater acoustic channels via low-rank recovery

Abstract

This paper presents a technique for solving the multichannel blind deconvolution problem. The authors observe the convolution of a single (unknown) source with K different (unknown) channel responses; from these channel outputs, the authors want to estimate both the source and the channel responses. The authors show how this classical signal processing problem can be viewed as solving a system of bilinear equations, and in turn can be recast as recovering a rank-1 matrix from a set of linear observations. Results of prior studies in the area of low-rank matrix recovery have identified effective convex relaxations for problems of this type and efficient, scalable heuristic solvers that enable these techniques to work with thousands of unknown variables. The authors show how a priori information about the channels can be used to build a linear model for the channels, which in turn makes solving these systems of equations well-posed. This study demonstrates the robustness of this methodology to measurement noises and parametrization errors of the channel impulse responses with several stylized and shallow water acoustic channel simulations. The performance of this methodology is also verified experimentally using shipping noise recorded on short bottom-mounted vertical line arrays.

Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness

“…Finally we study data obtained from a parametric channel impulse response model and apply SCCC under subspace model obtained empirically by principal component analysis [43]. More precisely, the unknown filters are generated by sampling a known continuous function with random shifts (not necessarily on a given grid) followed by scaling with random amplitudes.…”

“…Using a linear subspace to model the channel responses has had some empirical success in the literature. For example, in [43] a data-driven linear model is constructed for underwater acoustic channels for the purpose of ocean tomography.…”

Blind Deconvolution Using Modulated Inputs

“…The recorded data at each of the receivers in the passive imaging applications above takes the form 6 .…”

Multichannel Sparse Blind Deconvolution on the Sphere

“…Opportunistic underwater acoustics: Underwater acoustic channels are sparse in nature [23]. Estimating such sparse channels with an array of receivers using opportunistic sources (e.g., shipping noise) involves a blind deconvolution problem with multiple unknown sparse channels [24,25].…”

“…Previous approaches to MSBD have provided efficient iterative algorithms to compute maximum likelihood (ML) estimates of parametric models of the channels {x i } N i=1 [25], or maximum a posteriori (MAP) estimates in various Bayesian frameworks [15,26]. However, these algorithms usually do not have theoretical guarantees or sample complexity bounds.…”