A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery Article Swipe
Yue Hu
,
Xiaohan Liu
,
Mathews Jacob
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1811.10778
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1811.10778
Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix, respectively. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and memory efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches.
Related Topics
Concepts
Toeplitz matrix
Circulant matrix
Algorithm
Convolution (computer science)
Rank (graph theory)
Matrix (chemical analysis)
Mathematics
Low-rank approximation
Piecewise
Mathematical optimization
Hankel matrix
Computer science
Artificial intelligence
Mathematical analysis
Pure mathematics
Materials science
Artificial neural network
Combinatorics
Composite material
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1811.10778
- https://arxiv.org/pdf/1811.10778
- OA Status
- green
- References
- 29
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2949099302
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2949099302Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1811.10778Digital Object Identifier
- Title
-
A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image RecoveryWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2018Year of publication
- Publication date
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2018-11-27Full publication date if available
- Authors
-
Yue Hu, Xiaohan Liu, Mathews JacobList of authors in order
- Landing page
-
https://arxiv.org/abs/1811.10778Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1811.10778Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1811.10778Direct OA link when available
- Concepts
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Toeplitz matrix, Circulant matrix, Algorithm, Convolution (computer science), Rank (graph theory), Matrix (chemical analysis), Mathematics, Low-rank approximation, Piecewise, Mathematical optimization, Hankel matrix, Computer science, Artificial intelligence, Mathematical analysis, Pure mathematics, Materials science, Artificial neural network, Combinatorics, Composite materialTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
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29Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.recover | 33 |
| abstract_inverted_index.restore | 20 |
| abstract_inverted_index.results | 72 |
| abstract_inverted_index.satisfy | 67 |
| abstract_inverted_index.Toeplitz | 10, 76, 112, 129 |
| abstract_inverted_index.combined | 90 |
| abstract_inverted_index.constant | 54 |
| abstract_inverted_index.improved | 153 |
| abstract_inverted_index.indicate | 147 |
| abstract_inverted_index.low-rank | 9, 30, 82 |
| abstract_inverted_index.matrices | 86 |
| abstract_inverted_index.problem. | 93 |
| abstract_inverted_index.property | 83 |
| abstract_inverted_index.proposed | 150 |
| abstract_inverted_index.provides | 152 |
| abstract_inverted_index.recovery | 154 |
| abstract_inverted_index.Numerical | 145 |
| abstract_inverted_index.algorithm | 31, 121, 134, 151 |
| abstract_inverted_index.component | 55, 66 |
| abstract_inverted_index.effective | 17 |
| abstract_inverted_index.efficient | 120 |
| abstract_inverted_index.formulate | 88 |
| abstract_inverted_index.introduce | 26, 115 |
| abstract_inverted_index.matrices, | 113 |
| abstract_inverted_index.piecewise | 53, 58 |
| abstract_inverted_index.recovery. | 144 |
| abstract_inverted_index.relation, | 70 |
| abstract_inverted_index.resulting | 108 |
| abstract_inverted_index.component. | 60 |
| abstract_inverted_index.structured | 8, 29, 75 |
| abstract_inverted_index.approaches. | 159 |
| abstract_inverted_index.convolution | 42 |
| abstract_inverted_index.demonstrate | 132 |
| abstract_inverted_index.efficiently | 100 |
| abstract_inverted_index.experiments | 146 |
| abstract_inverted_index.generalized | 28 |
| abstract_inverted_index.large-scale | 111 |
| abstract_inverted_index.performance | 155 |
| abstract_inverted_index.regularized | 91 |
| abstract_inverted_index.annihilation | 69 |
| abstract_inverted_index.coefficients | 39, 63 |
| abstract_inverted_index.optimization | 92 |
| abstract_inverted_index.undersampled | 37 |
| abstract_inverted_index.approximation | 126 |
| abstract_inverted_index.multi-channel | 141 |
| abstract_inverted_index.respectively. | 78 |
| abstract_inverted_index.superposition | 50 |
| abstract_inverted_index.half-circulant | 125 |
| abstract_inverted_index.regularizations. | 43 |
| abstract_inverted_index.state-of-the-art | 158 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |