Spark Deficient Gabor Frame Provides a Novel Analysis Operator for Compressed Sensing
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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 compared to state-of-the-art window vectors of time-frequency analysis.
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