Journal article
Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion
IEEE transactions on medical imaging, Vol.36(10), pp.2087-2098
10/2017
DOI: 10.1109/TMI.2017.2726995
PMCID: PMC5821149
PMID: 28715328
Abstract
We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.
Details
- Title: Subtitle
- Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion
- Creators
- Arvind Balachandrasekaran - Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, USAVincent Magnotta - Department of Radiology, The University of Iowa, Iowa City, IA, USAMathews Jacob - Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, USA
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on medical imaging, Vol.36(10), pp.2087-2098
- DOI
- 10.1109/TMI.2017.2726995
- PMID
- 28715328
- PMCID
- PMC5821149
- NLM abbreviation
- IEEE Trans Med Imaging
- ISSN
- 0278-0062
- eISSN
- 1558-254X
- Publisher
- Institute of Electrical and Electronics Engineers
- Grant note
- NIH 1R01EB019961-01A1 / NIH (10.13039/100000070) ONR N00014-13-1-0202 / ONR (10.13039/100000006)
- Language
- English
- Date published
- 10/2017
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Psychiatry; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070446102771
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