@article{3063228,
    title = "Spark Deficient Gabor Frame Provides A Novel Analysis Operator For Compressed Sensing",
    author = "Kouni, V. and Rauhut, H.",
    journal = "Communications in Computer and Information Science",
    year = "2021",
    volume = "1517 CCIS",
    pages = "700-708",
    publisher = "Springer Science and Business Media Deutschland GmbH",
    doi = "10.1007/978-3-030-92310-5_81",
    keywords = "Artificial intelligence;  Computers, Analysis operators;  Analysis sparsities;  Compressed-Sensing;  Effective approaches;  Gabor frames;  Gabor transform;  Minimisation;  Sensing applications;  Spark deficient gabor frame;  Window vector, Compressed sensing",
    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 l1 -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 l1 -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. © 2021, Springer Nature Switzerland AG."
}