Coherence of randomly pre-conditioned matrices

Jampana, Phanindra Varma (2017) Coherence of randomly pre-conditioned matrices. In: Indian Control Conference, ICC, 4-6 January, 2017, Indian Institute of Technology (IIT) Guwahati Guwahati; India.

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Abstract

In many applications of compressed sensing, coherence of the matrix A plays an important role in theoretical guarantees for obtaining sparse solutions to linear system of equations, y = Ax. For a given matrix G with trivial right null space, the system Gy = GAx is equivalent. In this paper we establish that if G is a random matrix with i.i.d. realizations of Gaussian or Bernoulli random variables then the coherence of GA cannot be made smaller than the coherence of A with very high probability, in the limit when the row size of G tends to infinity. A similar result is also shown when G is a square random Gaussian matrix and its row size tends to infinity.

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IITH Creators:
IITH CreatorsORCiD
Jampana, Phanindra Varmahttp://orcid.org/0000-0002-9678-5249
Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Control Bernoulli random variables; Gaussian matrixes; High probability; Linear system of equations; Null space; Random Matrix; Sparse solutions; Theoretical guarantees
Subjects: Chemical Engineering > Biochemical Engineering
Divisions: Department of Chemical Engineering
Depositing User: Team Library
Date Deposited: 11 Apr 2017 05:11
Last Modified: 12 Sep 2017 08:38
URI: http://raiith.iith.ac.in/id/eprint/3155
Publisher URL: https://doi.org/10.1109/INDIANCC.2017.7846445
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