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A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery.
- Source :
-
IEEE Transactions on Medical Imaging . Aug2019, Vol. 38 Issue 1, p1841-1851. 11p. - Publication Year :
- 2019
-
Abstract
- 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. 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 a 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02780062
- Volume :
- 38
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Medical Imaging
- Publication Type :
- Academic Journal
- Accession number :
- 137913633
- Full Text :
- https://doi.org/10.1109/TMI.2018.2886290