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
Hauptverfasser: Luo, Jianhua, Mou, Zhiying, Qin, Binjie, Li, Wanqing, Ogunbona, Philip, Robini, Marc C., Zhu, Yuemin
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container_issue 7
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container_title Medical & biological engineering & computing
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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
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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. 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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. 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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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