Publication

MRI artifact correction using sparse plus low-rank decomposition of annihilating filter-based hankel matrix

Kyong Hwan Jin
2017
Journal Articles

Abstract

PurposeMagnetic 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. TheoryRecently, 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. MethodsThe 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. ResultsExperimental results demonstrated that the proposed algorithm can correct MR artifacts including herringbone (crisscross), motion, and zipper artifacts without image distortion. ConclusionThe 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. (c) 2016 International Society for Magnetic Resonance in Medicine

Official source

https://infoscience.epfl.ch/entities/publication/2700ee25-5db3-4f51-a720-6905654c28ec

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Kyong Hwan Jin
2017
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2700ee25-5db3-4f51-a720-6905654c28ec

About this result

Related concepts (32)

Low-rank approximation

In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.

Magnetic resonance imaging

Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from computed tomography (CT) and positron emission tomography (PET) scans.

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

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