Tensor denoising of multidimensional MRI data

Purpose To develop a denoising strategy leveraging redundancy in high‐dimensional data. Theory and Methods The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so‐called MPPCA: principal component...

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Published in:	Magnetic resonance in medicine Vol. 89; no. 3; pp. 1160 - 1172
Main Authors:	Olesen, Jonas L., Ianus, Andrada, Østergaard, Leif, Shemesh, Noam, Jespersen, Sune N.
Format:	Journal Article
Language:	English
Published:	United States Wiley Subscription Services, Inc 01.03.2023 John Wiley and Sons Inc
Subjects:	Algorithms Blurring Brain - diagnostic imaging denoising diffusion Diffusion Magnetic Resonance Imaging - methods Magnetic resonance imaging Magnetic Resonance Imaging - methods Mathematical analysis Multidimensional data Noise reduction Patches (structures) Phantoms, Imaging Principal Component Analysis Principal components analysis random matrix theory Redundancy Signal-To-Noise Ratio s—Computer Processing and Modeling Tensors denoising random matrix theory diffusion principal component analysis
ISSN:	0740-3194, 1522-2594, 1522-2594
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Abstract	Purpose To develop a denoising strategy leveraging redundancy in high‐dimensional data. Theory and Methods The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so‐called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko‐Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor‐structure to better characterize noise, and to recursively estimate signal components. Results Relative to matrix‐based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi‐TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases. Conclusions The MPPCA denoising technique can be extended to high‐dimensional data with improved performance for smaller patch sizes.
AbstractList	To develop a denoising strategy leveraging redundancy in high-dimensional data. The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so-called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko-Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor-structure to better characterize noise, and to recursively estimate signal components. Relative to matrix-based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi-TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases. The MPPCA denoising technique can be extended to high-dimensional data with improved performance for smaller patch sizes. PurposeTo develop a denoising strategy leveraging redundancy in high‐dimensional data.Theory and MethodsThe SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so‐called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko‐Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor‐structure to better characterize noise, and to recursively estimate signal components.ResultsRelative to matrix‐based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi‐TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases.ConclusionsThe MPPCA denoising technique can be extended to high‐dimensional data with improved performance for smaller patch sizes. Click here for author‐reader discussions Purpose To develop a denoising strategy leveraging redundancy in high‐dimensional data. Theory and Methods The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so‐called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko‐Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor‐structure to better characterize noise, and to recursively estimate signal components. Results Relative to matrix‐based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi‐TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases. Conclusions The MPPCA denoising technique can be extended to high‐dimensional data with improved performance for smaller patch sizes. To develop a denoising strategy leveraging redundancy in high-dimensional data.PURPOSETo develop a denoising strategy leveraging redundancy in high-dimensional data.The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so-called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko-Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor-structure to better characterize noise, and to recursively estimate signal components.THEORY AND METHODSThe SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so-called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the Marchenko-Pastur distribution of noise singular values. Operating on matrices comprised of data patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring, or nonlocal averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, such as from multicontrast acquisitions. Rather than combining dimensions in matrices, tMPPCA uses each dimension of the multidimensional data's inherent tensor-structure to better characterize noise, and to recursively estimate signal components.Relative to matrix-based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi-TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases.RESULTSRelative to matrix-based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi-TE diffusion MRI data set, tMPPCA dramatically improves denoising performance. This is particularly true for small data patches, suggesting that tMPPCA can be especially beneficial in such cases.The MPPCA denoising technique can be extended to high-dimensional data with improved performance for smaller patch sizes.CONCLUSIONSThe MPPCA denoising technique can be extended to high-dimensional data with improved performance for smaller patch sizes.
Author	Østergaard, Leif Jespersen, Sune N. Olesen, Jonas L. Shemesh, Noam Ianus, Andrada
AuthorAffiliation	3 Champalimaud Research Champalimaud Foundation Lisbon Portugal 1 Center of Functionally Integrative Neuroscience, Department of Clinical Medicine Aarhus University Aarhus Denmark 2 Department of Physics and Astronomy Aarhus University Aarhus Denmark
AuthorAffiliation_xml	– name: 1 Center of Functionally Integrative Neuroscience, Department of Clinical Medicine Aarhus University Aarhus Denmark – name: 3 Champalimaud Research Champalimaud Foundation Lisbon Portugal – name: 2 Department of Physics and Astronomy Aarhus University Aarhus Denmark
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Snippet	Purpose To develop a denoising strategy leveraging redundancy in high‐dimensional data. Theory and Methods The SNR fundamentally limits the information... Click here for author‐reader discussions To develop a denoising strategy leveraging redundancy in high-dimensional data. The SNR fundamentally limits the information accessible by MRI. This limitation... PurposeTo develop a denoising strategy leveraging redundancy in high‐dimensional data.Theory and MethodsThe SNR fundamentally limits the information accessible... To develop a denoising strategy leveraging redundancy in high-dimensional data.PURPOSETo develop a denoising strategy leveraging redundancy in high-dimensional...
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SubjectTerms	Algorithms Blurring Brain - diagnostic imaging denoising diffusion Diffusion Magnetic Resonance Imaging - methods Magnetic resonance imaging Magnetic Resonance Imaging - methods Mathematical analysis Multidimensional data Noise reduction Patches (structures) Phantoms, Imaging Principal Component Analysis Principal components analysis random matrix theory Redundancy Signal-To-Noise Ratio s—Computer Processing and Modeling Tensors
Title	Tensor denoising of multidimensional MRI data
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