Journal article
Convex Recovery of Continuous Domain Piecewise Constant Images From Nonuniform Fourier Samples
IEEE transactions on signal processing, Vol.66(1), pp.236-250
01/01/2018
DOI: 10.1109/TSP.2017.2750111
PMCID: PMC6101269
PMID: 30140146
Abstract
We consider the recovery of a continuous domain piecewise constant image from its nonuniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero level set of a bandlimited function. This assumption induces linear dependencies between the Fourier coefficients of the image, which results in a two-fold block Toeplitz matrix constructed from the Fourier coefficients being low rank. The proposed algorithm reformulates the recovery of the unknown Fourier coefficients as a structured low-rank matrix completion problem, where the nuclear norm of the matrix is minimized subject to structure and data constraints. We show that the exact recovery is possible with high probability when the edge set of the image satisfies an incoherency property. We also show that the incoherency property is dependent on the geometry of the edge set curve, implying higher sampling burden for smaller curves. This paper generalizes recent work on the super-resolution recovery of isolated Diracs or signals with finite rate of innovation to the recovery of piecewise constant images.
Details
- Title: Subtitle
- Convex Recovery of Continuous Domain Piecewise Constant Images From Nonuniform Fourier Samples
- Creators
- Greg Ongie - Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USASampurna Biswas - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USAMathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on signal processing, Vol.66(1), pp.236-250
- DOI
- 10.1109/TSP.2017.2750111
- PMID
- 30140146
- PMCID
- PMC6101269
- NLM abbreviation
- IEEE Trans Signal Process
- ISSN
- 1053-587X
- eISSN
- 1941-0476
- Publisher
- IEEE
- Grant note
- N00014-13-1-0202 / ONR (10.13039/100000006) 1R01EB019961-01A1 / NIH (10.13039/100000002)
- Language
- English
- Date published
- 01/01/2018
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070526002771
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