Sasmal, P and Theeda, P and Jampana, PV and Sastry, CS (2021) Nullspace Property for Optimality of Minimum Frame Angle under Invertible Linear Operators. In: IEEE Signal Processing Letters, 28 . pp. 1928-1932.
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Abstract
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.
| Item Type: | Journal Article |
|---|---|
| Publication: | IEEE Signal Processing Letters |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Compressed sensing, Absolute values; Compressed-Sensing; Equivalent frame; Linear operators; Minimum frame angle; Null space; Optimality; Preconditioning; Property; Semi-definite programming, Mathematical operators |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 01 Jun 2023 09:36 |
| Last Modified: | 01 Jun 2023 09:36 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81731 |
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