Conference proceeding
Recovery of piecewise smooth images from few fourier samples
2015 International Conference on Sampling Theory and Applications (SampTA), pp.543-547
05/2015
DOI: 10.1109/SAMPTA.2015.7148950
Abstract
We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples. Assuming the discontinuity set of the image is localized to the zero level-set of a trigonometric polynomial, we show the Fourier transform coefficients of partial derivatives of the signal satisfy an annihilation relation. We present necessary and sufficient conditions for unique recovery of piecewise constant images using the above annihilation relation. We pose the recovery of the Fourier coefficients of the signal from the measurements as a convex matrix completion algorithm, which relies on the lifting of the Fourier data to a structured low-rank matrix; this approach jointly estimates the signal and the annihilating filter. Finally, we demonstrate our algorithm on the recovery of MRI phantoms from few low-resolution Fourier samples.
Details
- Title: Subtitle
- Recovery of piecewise smooth images from few fourier samples
- Creators
- Greg Ongie - Dept. of Math., Univ. of Iowa, Iowa City, IA, USAMathews Jacob - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USA
- Resource Type
- Conference proceeding
- Publication Details
- 2015 International Conference on Sampling Theory and Applications (SampTA), pp.543-547
- DOI
- 10.1109/SAMPTA.2015.7148950
- Publisher
- IEEE
- Language
- English
- Date published
- 05/2015
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070503702771
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