- Title
- Sparse deconvolution via off-grid T.V minimization
- Creator
- Mahata, Kaushik; Hyder, Md Mashud
- Relation
- ARC.DP130103909 http://purl.org/au-research/grants/arc/DP130103909
- Relation
- Signal Processing Vol. 170, no. 107406
- Publisher Link
- http://dx.doi.org/10.1016/j.sigpro.2019.107406
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2020
- Description
- We present a grid-less solution to the total variation minimization approach to the sparse deconvolution problem. Unlike the existing methods [1, 2], our algorithm works directly with time domain data, and does not suffer from the consequences of leakage errors incurred while transforming the time domain measurements to frequency domain. The total variation minimization problem requires us to optimize the total variation of a function. This is an infinite dimensional problem. To deal with the underlying infinite dimensionality, we consider its finite dimensional semi-infinite duals with point-wise constraints. We provide a finite parameterization to handle the point-wise constraints in a computationally tractable manner. This parameterization exploits the underlying bandlimitedness of the convolution kernel by employing Prolate Spheroidal Wave Functions. Consequently, we are able to reduce the total variation minimization problem into a semidefinite program, which can be solved in polynomial time. We demonstrate its utility via numerical simulation studies as well as real world signal reconstruction examples.
- Subject
- sparse deconvolution; super resolution; Prolate spheroidal wave functions; off-grid
- Identifier
- http://hdl.handle.net/1959.13/1438422
- Identifier
- uon:40604
- Identifier
- ISSN:0165-1684
- Language
- eng
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