Identification of Matrices Having a Sparse Representation

  • Authors:
  • G.E. Pfander;H. Rauhut;J. Tanner

  • Affiliations:
  • Sch. of Eng. & Sci., Jacobs Univ., Bremen;-;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2008

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Abstract

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.