# Structured matrix approximation problems in signal processing

#### Abstract

Several well known problems in signal processing are formulated within a general framework of structured matrix approximation problems. The general problem is stated as follows: Given an N x M matrix X of rank $r\le min(N,M),$ where N = number of rows and M = number of columns of X, it is required to find another N x M matrix X with known rank $\~r\le r,$ such that $\Vert{\bf X} - {\bf \tilde X}\Vert\sbsp{F}{2}$ (the Frobenius matrix norm) is minimized. The rows and/or the columns of the approximating matrix X are required to span subspaces with specified structures. The subspaces are chosen from prior knowledge about the particular signal processing problem under consideration.^ The following problems formulated within the structured matrix approximation framework are covered in this dissertation: Frequency Estimation, Angles of Arrival Estimation, Frequency-Wavenumber Estimation, Toeplitz/Hankel Matrix Approximation and Broadband Source Localization. It is demonstrated that a computationally simple iterative algorithm is commonly applicable to all the problems formulated in this general framework. The performance of the proposed approach will be compared with existing results and theoretical bounds with several computer simulations. ^

#### Subject Area

Engineering, Electronics and Electrical

#### Recommended Citation

Arnab Kumar Shaw, "Structured matrix approximation problems in signal processing" (1987). Dissertations and Master's Theses (Campus Access). Paper AAI9302662.
http://digitalcommons.uri.edu/dissertations/AAI9302662

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