Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery
We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation...
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Veröffentlicht in: | IEEE transactions on medical imaging 2019-04, Vol.38 (4), p.979-990 |
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description | We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced. |
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We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.</description><identifier>ISSN: 0278-0062</identifier><identifier>EISSN: 1558-254X</identifier><identifier>DOI: 10.1109/TMI.2018.2876423</identifier><identifier>PMID: 30334785</identifier><identifier>CODEN: ITMID4</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject>Algorithms ; annihilation filter ; Brain - diagnostic imaging ; Calibration ; Compensation ; Data recovery ; Distortion ; Echo-Planar Imaging - methods ; EPI artifacts ; Fourier series ; Humans ; Image processing ; Image Processing, Computer-Assisted - methods ; Image segmentation ; Inhomogeneity ; Magnetic resonance imaging ; Matrix algebra ; matrix completion ; Matrix methods ; Nonhomogeneous media ; Phantoms, Imaging ; Pixels ; Recovery (Medical) ; regularized recovery ; Signal Processing, Computer-Assisted ; Smoothness ; structured low rank ; Time measurement ; Time series ; Toeplitz matrix ; Transmission line matrix methods ; Vectors (mathematics)</subject><ispartof>IEEE transactions on medical imaging, 2019-04, Vol.38 (4), p.979-990</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.</description><subject>Algorithms</subject><subject>annihilation filter</subject><subject>Brain - diagnostic imaging</subject><subject>Calibration</subject><subject>Compensation</subject><subject>Data recovery</subject><subject>Distortion</subject><subject>Echo-Planar Imaging - methods</subject><subject>EPI artifacts</subject><subject>Fourier series</subject><subject>Humans</subject><subject>Image processing</subject><subject>Image Processing, Computer-Assisted - methods</subject><subject>Image segmentation</subject><subject>Inhomogeneity</subject><subject>Magnetic resonance imaging</subject><subject>Matrix algebra</subject><subject>matrix completion</subject><subject>Matrix methods</subject><subject>Nonhomogeneous media</subject><subject>Phantoms, Imaging</subject><subject>Pixels</subject><subject>Recovery (Medical)</subject><subject>regularized recovery</subject><subject>Signal Processing, Computer-Assisted</subject><subject>Smoothness</subject><subject>structured low rank</subject><subject>Time measurement</subject><subject>Time series</subject><subject>Toeplitz matrix</subject><subject>Transmission line matrix methods</subject><subject>Vectors (mathematics)</subject><issn>0278-0062</issn><issn>1558-254X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><sourceid>EIF</sourceid><recordid>eNpdkd9v0zAQxy0EYt3GOxISssTLXlLOvxrnBWmUDSp12rR1Em_WxbkMjzQeTjLYf0-qlgp4suz73Fd3_jD2WsBUCCjery4WUwnCTqXNZ1qqZ2wijLGZNPrrczYBmdsMYCYP2GHX3QMIbaB4yQ4UKKVzayZsNccmlAn7ENvsPBHxj8DnMSXymycea352teCfsEd-24X2jt_0afD9kKjiy_iTX2P7nV9gn8Ivfk0-PlJ6OmYvamw6erU7j9jt-dlq_iVbXn5ezE-XmTcC-kxigaVBQfmszg2Ar6gExHG4qvRWq9oXUpcC0Ra1Gm-zvDSmkt4YqgmlUEfswzb3YSjXVHlq-4SNe0hhjenJRQzu30obvrm7-Ohyq8e_sGPAyS4gxR8Ddb1bh85T02BLceicFFIaazTAiL77D72PQ2rH9ZyUoDTIQm4o2FI-xa5LVO-HEeA2ytyozG2UuZ2yseXt30vsG_44GoE3WyAQ0b5sdaFMDuo3QauajA</recordid><startdate>20190401</startdate><enddate>20190401</enddate><creator>Balachandrasekaran, Arvind</creator><creator>Mani, Merry</creator><creator>Jacob, Mathews</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Mani, Merry ; Jacob, Mathews</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c510t-2a9ab5a1e76f7500cdeb0aa303dbc843fc924b1aa89f33fc67b55d2c55efea213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>annihilation filter</topic><topic>Brain - diagnostic imaging</topic><topic>Calibration</topic><topic>Compensation</topic><topic>Data recovery</topic><topic>Distortion</topic><topic>Echo-Planar Imaging - methods</topic><topic>EPI artifacts</topic><topic>Fourier series</topic><topic>Humans</topic><topic>Image processing</topic><topic>Image Processing, Computer-Assisted - methods</topic><topic>Image segmentation</topic><topic>Inhomogeneity</topic><topic>Magnetic resonance imaging</topic><topic>Matrix algebra</topic><topic>matrix completion</topic><topic>Matrix methods</topic><topic>Nonhomogeneous media</topic><topic>Phantoms, Imaging</topic><topic>Pixels</topic><topic>Recovery (Medical)</topic><topic>regularized recovery</topic><topic>Signal Processing, Computer-Assisted</topic><topic>Smoothness</topic><topic>structured low rank</topic><topic>Time measurement</topic><topic>Time series</topic><topic>Toeplitz matrix</topic><topic>Transmission line matrix methods</topic><topic>Vectors (mathematics)</topic><toplevel>online_resources</toplevel><creatorcontrib>Balachandrasekaran, Arvind</creatorcontrib><creatorcontrib>Mani, Merry</creatorcontrib><creatorcontrib>Jacob, Mathews</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Nursing & Allied Health Premium</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>IEEE transactions on medical imaging</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Balachandrasekaran, Arvind</au><au>Mani, Merry</au><au>Jacob, Mathews</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery</atitle><jtitle>IEEE transactions on medical imaging</jtitle><stitle>TMI</stitle><addtitle>IEEE Trans Med Imaging</addtitle><date>2019-04-01</date><risdate>2019</risdate><volume>38</volume><issue>4</issue><spage>979</spage><epage>990</epage><pages>979-990</pages><issn>0278-0062</issn><eissn>1558-254X</eissn><coden>ITMID4</coden><abstract>We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. 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subjects | Algorithms annihilation filter Brain - diagnostic imaging Calibration Compensation Data recovery Distortion Echo-Planar Imaging - methods EPI artifacts Fourier series Humans Image processing Image Processing, Computer-Assisted - methods Image segmentation Inhomogeneity Magnetic resonance imaging Matrix algebra matrix completion Matrix methods Nonhomogeneous media Phantoms, Imaging Pixels Recovery (Medical) regularized recovery Signal Processing, Computer-Assisted Smoothness structured low rank Time measurement Time series Toeplitz matrix Transmission line matrix methods Vectors (mathematics) |
title | Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery |
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