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Spark Deficient Gabor Frame Provides A Novel Analysis Operator For Compressed Sensing

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Neural Information Processing (ICONIP 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1517))

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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 frame, is a new (highly) redundant Gabor transform, which we use as a sparsifier 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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Notes

  1. 1.

    in terms of optimization, it is preferred to solve (2) instead of (3).

  2. 2.

    \(bb^{-1}\equiv 1(\mathrm {mod}L)\).

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Authors and Affiliations

  1. Chair for Mathematics of Information Processing, RWTH Aachen University, Aachen, Germany

    Vasiliki Kouni & Holger Rauhut

  2. Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece

    Vasiliki Kouni

Authors
  1. Vasiliki Kouni
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  2. Holger Rauhut
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Corresponding author

Correspondence to Vasiliki Kouni .

Editor information

Editors and Affiliations

  1. Sampoerna University, Jakarta, Indonesia

    Teddy Mantoro

  2. Kyungpook National University, Daegu, Korea (Republic of)

    Minho Lee

  3. Sampoerna University, Jakarta, Indonesia

    Media Anugerah Ayu

  4. Murdoch University, Murdoch, WA, Australia

    Kok Wai Wong

  5. Universitas Indonesia, Depok, Indonesia

    Achmad Nizar Hidayanto

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Kouni, V., Rauhut, H. (2021). Spark Deficient Gabor Frame Provides A Novel Analysis Operator For Compressed Sensing. In: Mantoro, T., Lee, M., Ayu, M.A., Wong, K.W., Hidayanto, A.N. (eds) Neural Information Processing. ICONIP 2021. Communications in Computer and Information Science, vol 1517. Springer, Cham. https://doi.org/10.1007/978-3-030-92310-5_81

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  • DOI: https://doi.org/10.1007/978-3-030-92310-5_81

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  • Online ISBN: 978-3-030-92310-5

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