Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators

Sasmal, Pradip and Theeda, Prasad and Jampana, Phanindra Varma and Sastry, Challa Subrahmanya (2021) Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators. IEEE Signal Processing Letters, 28. pp. 1928-1932. ISSN 1070-9908

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Frames with a large minimum angle between any two distinct frame vectors are desirable in many present day applications. For a unit norm frame, the absolute value of the cosine of the minimum frame angle is also known as coherence. Two frames are equivalent if one can be obtained from the other via left action of an invertible linear operator. Frame angles can change under the action of a linear operator. Most of the existing works solve different optimization problems to find an optimal linear operator that maximizes the minimal frame angle (in other words, minimizes the coherence). In the present work, nevertheless, we consider the question: Is it always possible to find an equivalent frame with smaller coherence for a given frame?. In this paper, we derive properties of the initial unit norm frame that can ensure an equivalent frame with strictly larger minimal frame angle compared to the initial one. It turns out that the nullspace property of a certain matrix obtained from the initial frame can guarantee such an equivalent frame. We also present the numerical results that support our theoretical claims. © 1994-2012 IEEE.

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IITH Creators:
IITH CreatorsORCiD
Jampana, Phanindra Varma
Sastry, Challa SubrahmanyaUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: coherence; compressed sensing; Minimum frame angle; preconditioning; semidefinite programming
Subjects: Mathematics
Chemical Engineering
Divisions: Department of Chemical Engineering
Department of Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 10 Sep 2022 10:01
Last Modified: 10 Sep 2022 10:01
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