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arXiv · 2103.11233

Spark Deficient Gabor Frame Provides a Novel Analysis Operator for Compressed Sensing

Vasiliki Kouni·Holger Rauhut
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Abstract

The analysis sparsity model is a very effective approach in modern Compressed Sensing applications. Specifically, redundant analysis operators can lead to fewer measurements needed for reconstruction when employing the analysis $l_1$-minimization in Compressed Sensing. In this paper, we pick an eigenvector of the Zauner unitary matrix and -- under certain assumptions on the ambient dimension -- we build a spark deficient Gabor frame. The analysis operator associated with such a spark deficient Gabor frame, is a new (highly) redundant Gabor transform, which we use as a sparsifying transform in Compressed Sensing. We conduct computational experiments -- on both synthetic and real-world data -- solving the analysis $l_1$-minimization problem of Compressed Sensing, with four different choices of analysis operators, including our Gabor analysis operator. The results show that our proposed redundant Gabor transform outperforms -- in all cases -- Gabor transforms generated by state-of-the-art window vectors of time-frequency analysis.

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Vasiliki Kouni, Holger Rauhut. 2021-03-20. Spark Deficient Gabor Frame Provides a Novel Analysis Operator for Compressed Sensing. https://doi.org/10.1007/978-3-030-92310-5_81

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