Using the LASSO's Dual for Regularization in Sparse Signal Reconstruction from Array Data

TL;DR

This paper introduces a dual-based approach for selecting the regularization parameter in complex-valued LASSO to improve sparse source localization from array data, with algorithms for estimating source directions of arrival.

Contribution

It formulates the dual problem of complex LASSO and develops algorithms for regularization parameter selection and source DOA estimation, enhancing sparse signal reconstruction methods.

Findings

Dual solution aids in regularization parameter selection.

Proposed algorithms accurately estimate source DOAs.

Method improves sparse signal reconstruction from array data.

Abstract

Waves from a sparse set of source hidden in additive noise are observed by a sensor array. We treat the estimation of the sparse set of sources as a generalized complex-valued LASSO problem. The corresponding dual problem is formulated and it is shown that the dual solution is useful for selecting the regularization parameter of the LASSO when the number of sources is given. The solution path of the complex-valued LASSO is analyzed. For a given number of sources, the corresponding regularization parameter is determined by an order-recursive algorithm and two iterative algorithms that are based on a further approximation. Using this regularization parameter, the DOAs of all sources are estimated.