A Weighted Generalized Coherence Approach for Sensing Matrix Design
- URL: http://arxiv.org/abs/2110.02645v1
- Date: Wed, 6 Oct 2021 10:44:21 GMT
- Title: A Weighted Generalized Coherence Approach for Sensing Matrix Design
- Authors: Ameya Anjarlekar, Ajit Rajwade
- Abstract summary: We propose generalizations of the well-known mutual coherence criterion for optimizing sensing matrices.
An algorithm is also presented to solve the optimization problems.
- Score: 2.3478438171452014
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: As compared to using randomly generated sensing matrices, optimizing the
sensing matrix w.r.t. a carefully designed criterion is known to lead to better
quality signal recovery given a set of compressive measurements. In this paper,
we propose generalizations of the well-known mutual coherence criterion for
optimizing sensing matrices starting from random initial conditions. We term
these generalizations as bi-coherence or tri-coherence and they are based on a
criterion that discourages any one column of the sensing matrix from being
close to a sparse linear combination of other columns. We also incorporate
training data to further improve the sensing matrices through weighted
coherence, weighted bi-coherence, or weighted tri-coherence criteria, which
assign weights to sensing matrix columns as per their importance. An algorithm
is also presented to solve the optimization problems. Finally, the
effectiveness of the proposed algorithm is demonstrated through empirical
results.
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