Iteratively reweighted least squares for reconstruction of low-rank matrices with linear structure

Abstract

This paper considers the problem of reconstructing low-rank matrices from undersampled measurements, when the matrix has a known linear structure. Based on the iterative reweighted least-squares approach, we develop an algorithm that exploits the linear structure in an efficient way that allows for reconstruction in highly undersampled scenarios. The method also enables inferring an appropriate regularization parameter value from the observations. The performance of the method is tested in a missing data recovery problem.

Enhanced Capon beamformer using regularized covariance matching

“…We now present an approximate iterative solution to (4) drawing upon on [9]. First, note that a Hermitian Toeplitz matrix can be written as…”

“…This enables the formulation of a regularized covariance matching problem which is solved approximately by an iteratively reweighted technique, cf. [7], [8], [9]. The resulting covariance matrix estimate and the Capon beamformer are evaluate by means of simulations.…”