A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data
Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of...
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Veröffentlicht in: | Medical & biological engineering & computing 2018-07, Vol.56 (7), p.1211-1225 |
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creator | Luo, Jianhua Mou, Zhiying Qin, Binjie Li, Wanqing Ogunbona, Philip Robini, Marc C. Zhu, Yuemin |
description | Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data.
Graphical abstract
Two Real Images and their sparsified images by singularizing operator |
doi_str_mv | 10.1007/s11517-017-1763-2 |
format | Article |
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Graphical abstract
Two Real Images and their sparsified images by singularizing operator</description><identifier>ISSN: 0140-0118</identifier><identifier>EISSN: 1741-0444</identifier><identifier>DOI: 10.1007/s11517-017-1763-2</identifier><identifier>PMID: 29222614</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Biomedical and Life Sciences ; Biomedical Engineering and Bioengineering ; Biomedicine ; Brain ; Computer Applications ; Computer Science ; Elastic Modulus ; Entrepreneurs ; Fourier transforms ; Human Physiology ; Image processing ; Image Processing, Computer-Assisted ; Image quality ; Image reconstruction ; Imaging ; Magnetic Resonance Imaging ; Mathematical models ; Medical Imaging ; Models, Theoretical ; Noise levels ; Operators ; Original Article ; Parameter estimation ; Phantoms, Imaging ; Radiology ; Resonance ; Signal-To-Noise Ratio</subject><ispartof>Medical & biological engineering & computing, 2018-07, Vol.56 (7), p.1211-1225</ispartof><rights>International Federation for Medical and Biological Engineering 2017</rights><rights>Medical & Biological Engineering & Computing is a copyright of Springer, (2017). All Rights Reserved.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c406t-10f361fa01bc651a7720c6edc0306101891a117c20021d93769fae767a5c0e133</citedby><cites>FETCH-LOGICAL-c406t-10f361fa01bc651a7720c6edc0306101891a117c20021d93769fae767a5c0e133</cites><orcidid>0000-0001-7445-1582 ; 0000-0002-7317-9641 ; 0000-0002-5217-493X ; 0000-0001-6814-1449</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11517-017-1763-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11517-017-1763-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/29222614$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-02071570$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Luo, Jianhua</creatorcontrib><creatorcontrib>Mou, Zhiying</creatorcontrib><creatorcontrib>Qin, Binjie</creatorcontrib><creatorcontrib>Li, Wanqing</creatorcontrib><creatorcontrib>Ogunbona, Philip</creatorcontrib><creatorcontrib>Robini, Marc C.</creatorcontrib><creatorcontrib>Zhu, Yuemin</creatorcontrib><title>A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data</title><title>Medical & biological engineering & computing</title><addtitle>Med Biol Eng Comput</addtitle><addtitle>Med Biol Eng Comput</addtitle><description>Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data.
Graphical abstract
Two Real Images and their sparsified images by singularizing operator</description><subject>Algorithms</subject><subject>Biomedical and Life Sciences</subject><subject>Biomedical Engineering and Bioengineering</subject><subject>Biomedicine</subject><subject>Brain</subject><subject>Computer Applications</subject><subject>Computer Science</subject><subject>Elastic Modulus</subject><subject>Entrepreneurs</subject><subject>Fourier transforms</subject><subject>Human Physiology</subject><subject>Image processing</subject><subject>Image Processing, Computer-Assisted</subject><subject>Image quality</subject><subject>Image reconstruction</subject><subject>Imaging</subject><subject>Magnetic Resonance Imaging</subject><subject>Mathematical models</subject><subject>Medical Imaging</subject><subject>Models, Theoretical</subject><subject>Noise levels</subject><subject>Operators</subject><subject>Original Article</subject><subject>Parameter estimation</subject><subject>Phantoms, 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singular K-space model for fast reconstruction of magnetic resonance images from undersampled data</title><author>Luo, Jianhua ; Mou, Zhiying ; Qin, Binjie ; Li, Wanqing ; Ogunbona, Philip ; Robini, Marc C. ; Zhu, Yuemin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c406t-10f361fa01bc651a7720c6edc0306101891a117c20021d93769fae767a5c0e133</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algorithms</topic><topic>Biomedical and Life Sciences</topic><topic>Biomedical Engineering and Bioengineering</topic><topic>Biomedicine</topic><topic>Brain</topic><topic>Computer Applications</topic><topic>Computer Science</topic><topic>Elastic Modulus</topic><topic>Entrepreneurs</topic><topic>Fourier transforms</topic><topic>Human Physiology</topic><topic>Image processing</topic><topic>Image Processing, Computer-Assisted</topic><topic>Image quality</topic><topic>Image 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Comput</addtitle><date>2018-07-01</date><risdate>2018</risdate><volume>56</volume><issue>7</issue><spage>1211</spage><epage>1225</epage><pages>1211-1225</pages><issn>0140-0118</issn><eissn>1741-0444</eissn><abstract>Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data.
Graphical abstract
Two Real Images and their sparsified images by singularizing operator</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><pmid>29222614</pmid><doi>10.1007/s11517-017-1763-2</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0001-7445-1582</orcidid><orcidid>https://orcid.org/0000-0002-7317-9641</orcidid><orcidid>https://orcid.org/0000-0002-5217-493X</orcidid><orcidid>https://orcid.org/0000-0001-6814-1449</orcidid></addata></record> |
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subjects | Algorithms Biomedical and Life Sciences Biomedical Engineering and Bioengineering Biomedicine Brain Computer Applications Computer Science Elastic Modulus Entrepreneurs Fourier transforms Human Physiology Image processing Image Processing, Computer-Assisted Image quality Image reconstruction Imaging Magnetic Resonance Imaging Mathematical models Medical Imaging Models, Theoretical Noise levels Operators Original Article Parameter estimation Phantoms, Imaging Radiology Resonance Signal-To-Noise Ratio |
title | A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data |
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