Identification of Matrices Having a Sparse Representation

We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of efficient reconstruction techniques such as Basis Pursuit. Of particular interest is the dictionary of time-frequency shift matrices and its role for channel estimation and identification in communications engineering. We present recovery results for Basis Pursuit with the time-frequency shift dictionary and various dictionaries of random matrices.

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Götz E. Pfander, Holger Rauhut, Jared Tanner
• Keywords: Basis Pursuit, Matrix, Time-frequency Shift, TSP 2008