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MRI artifact correction using sparse + low‐rank decomposition of annihilating filter‐based hankel matrix
Author(s) -
Jin Kyong Hwan,
Um JiYong,
Lee Dongwook,
Lee Juyoung,
Park SungHong,
Ye Jong Chul
Publication year - 2017
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.26330
Subject(s) - hankel matrix , computer science , artifact (error) , outlier , algorithm , matrix decomposition , compressed sensing , low rank approximation , matrix (chemical analysis) , filter (signal processing) , sparse matrix , rank (graph theory) , artificial intelligence , mathematics , computer vision , physics , mathematical analysis , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , gaussian , combinatorics
Purpose Magnetic resonance imaging (MRI) artifacts are originated from various sources including instability of an magnetic resonance (MR) system, patient motion, inhomogeneities of gradient fields, and so on. Such MRI artifacts are usually considered as irreversible, so additional artifact‐free scan or navigator scan is necessary. To overcome these limitations, this article proposes a novel compressed sensing‐based approach for removal of various MRI artifacts. Theory Recently, the annihilating filter based low‐rank Hankel matrix approach was proposed. The annihilating filter based low‐rank Hankel matrix exploits the duality between the low‐rankness of weighted Hankel structured matrix and the sparsity of signal in a transform domain. Because MR artifacts usually appeared as sparse k‐space components, the low‐rank Hankel matrix from underlying artifact‐free k‐space data can be exploited to decompose the sparse outliers. Methods The sparse + low‐rank decomposition framework using Hankel matrix was proposed for removal of MRI artifacts. Alternating direction method of multipliers algorithm was employed for the minimization of associated cost function with the initialized matrices from a factorization‐based matrix completion. Results Experimental results demonstrated that the proposed algorithm can correct MR artifacts including herringbone (crisscross), motion, and zipper artifacts without image distortion. Conclusion The proposed method may be a robust correction solution for various MRI artifacts that can be represented as sparse outliers. Magn Reson Med 78:327–340, 2017. © 2016 International Society for Magnetic Resonance in Medicine