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- W3199147857 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." @default.
- W3199147857 created "2021-09-27" @default.
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- W3199147857 date "2021-01-01" @default.
- W3199147857 modified "2023-10-16" @default.
- W3199147857 title "Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators" @default.
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- W3199147857 doi "https://doi.org/10.1109/lsp.2021.3112105" @default.
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