Construction of Structured Incoherent Unit Norm Tight Frames

Sasmal, P and Jampana, Phanindra Varma and Challa, Subrahmanya Sastry (2017) Construction of Structured Incoherent Unit Norm Tight Frames. arXiv.

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Abstract

The exact recovery property of Basis pursuit (BP) and Orthogonal Matching Pursuit (OMP) has a relation with the coherence of the underlying frame. A frame with low coherence provides better guarantees for exact recovery. In particular, Incoherent Unit Norm Tight Frames (IUNTFs) play a significant role in sparse representations. IUNTFs with special structure, in particular those given by a union of several orthonormal bases, are known to satisfy better theoretical guarantees for recovering sparse signals. In the present work, we propose to construct structured IUNTFs consisting of large number of orthonormal bases. For a given r,k,m with k being less than or equal to the smallest prime power factor of m and r<k, we construct a CS matrix of size mk×(mk×mr) with coherence at most rk, which consists of mr number of orthonormal bases and with density 1m. We also present numerical results of recovery performance of union of orthonormal bases as against their Gaussian counterparts.

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IITH Creators:
IITH CreatorsORCiD
Jampana, Phanindra Varmahttp://orcid.org/0000-0002-9678-5249
Challa, Subrahmanya SastryUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: numerical analysis
Subjects: Mathematics
Chemical Engineering
Divisions: Department of Chemical Engineering
Department of Mathematics
Depositing User: Team Library
Date Deposited: 10 Jul 2017 04:59
Last Modified: 01 Sep 2017 09:44
URI: http://raiith.iith.ac.in/id/eprint/3358
Publisher URL:
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