Conference proceeding
Coprime conditions for Fourier sampling for sparse recovery
2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp.533-536
06/2014
DOI: 10.1109/SAM.2014.6882460
Abstract
This paper considers the spark of L × N submatrices of the N × N Discrete Fourier Transform (DFT) matrix. Here a matrix has spark m if every collection of its m - 1 columns are linearly independent. The motivation comes from such applications of compressed sensing as MRI and synthetic aperture radar, where device physics dictates the measurements to be Fourier samples of the signal. Consequently the observation matrix comprises certain rows of the DFT matrix. To recover an arbitrary k-sparse signal, the spark of the observation matrix must exceed 2k + 1. The technical question addressed in this paper is how to choose the rows of the DFT matrix so that its spark equals the maximum possible value L + 1. We expose certain coprimeness conditions that guarantee such a property.
Details
- Title: Subtitle
- Coprime conditions for Fourier sampling for sparse recovery
- Creators
- Hema K Achanta - Dept. of Math., Univ. of Iowa, Iowa City, IA, USASampurna Biswas - Dept. of Math., Univ. of Iowa, Iowa City, IA, USASoura Dasgupta - Dept. of Math., Univ. of Iowa, Iowa City, IA, USAMathews Jacob - Dept. of Math., Univ. of Iowa, Iowa City, IA, USABhanumati N Dasgupta - Dept. of Math., Univ. of Iowa, Iowa City, IA, USARaghuraman Mudumbai - Dept. of Math., Univ. of Iowa, Iowa City, IA, USA
- Resource Type
- Conference proceeding
- Publication Details
- 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp.533-536
- Publisher
- IEEE
- DOI
- 10.1109/SAM.2014.6882460
- ISSN
- 1551-2282
- eISSN
- 2151-870X
- Language
- English
- Date published
- 06/2014
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Mathematics; Radiation Oncology; Iowa Neuroscience Institute; Radiology; Electrical and Computer Engineering
- Record Identifier
- 9984070691002771
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