"Spark Deficient Gabor Frames for Inverse Problems"Kouni, VasilikiIn this paper, we address two inverse problems: analysis Compressed Sensing and speech denoising. Both problems' approach is based on a redundant, analysis-sparse representation of the original signals of interest. We pick an eigenvector of the Zauner unitary matrix and --under certain assumptions on the ambient dimension-- we use it as window vector to generate a spark deficient Gabor frame. The analysis operator associated with such a frame, is a (highly) redundant Gabor transform, which we use as a sparsifying transform in both analysis Compressed Sensing and speech denoising procedures. We conduct computational experiments on synthetic and real-world data, solving the analysis $l_1$-minimization and analysis basis pursuit for Compressed Sensing and speech denoising problems respectively, 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. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Kouni_2021-06_Spark Deficient Gabor Frames for Inverse Problems.pdf |
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