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

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.

Reference-free single-pass EPI Nyquist ghost correction using annihilating filter-based low rank Hankel matrix (ALOHA).

PURPOSE: MR measurements from an echo-planar imaging (EPI) sequence produce Nyquist ghost artifacts that originate from inconsistencies between odd and even echoes. Several reconstruction algorithms have been proposed to reduce such artifacts, but most of these methods require either additional reference scans or multipass EPI acquisition. This article proposes a novel and accurate single-pass EPI ghost artifact correction method that does not require any additional reference data. THEORY AND METHODS: After converting a ghost correction problem into separate k-space data interpolation problems for even and odd phase encoding, our algorithm exploits an observation that the differential k-space data between the even and odd echoes is a Fourier transform of an underlying sparse image. Accordingly, we can construct a rank-deficient Hankel structured matrix, whose missing data can be recovered using an annihilating filter-based low rank Hankel structured matrix completion approach. RESULTS: The proposed method was applied to EPI data for both single and multicoil acquisitions. Experimental results using in vivo data confirmed that the proposed method can completely remove ghost artifacts successfully without prescan echoes. CONCLUSION: Owing to the discovery of the annihilating filter relationship from the intrinsic EPI image property, the proposed method successfully suppresses ghost artifacts without a prescan step. Magn Reson Med 76:1775-1789, 2016. © 2016 International Society for Magnetic Resonance in Medicine.