A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy
Abstract The nuclear magnetic resonance (NMR) spectroscopy has fruitful applications in chemistry, biology and life sciences, but suffers from long acquisition time. Non‐uniform sampling is a typical fast NMR method by undersampling the time‐domain data of the spectrum but need to restore the fully...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi-IET
2021-02-01
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| Series: | IET Signal Processing |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/sil2.12010 |
| _version_ | 1797427062382788608 |
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| author | Zhangren Tu Zi Wang Jiaying Zhan Yihui Huang Xiaofeng Du Min Xiao Xiaobo Qu Di Guo |
| author_facet | Zhangren Tu Zi Wang Jiaying Zhan Yihui Huang Xiaofeng Du Min Xiao Xiaobo Qu Di Guo |
| author_sort | Zhangren Tu |
| collection | DOAJ |
| description | Abstract The nuclear magnetic resonance (NMR) spectroscopy has fruitful applications in chemistry, biology and life sciences, but suffers from long acquisition time. Non‐uniform sampling is a typical fast NMR method by undersampling the time‐domain data of the spectrum but need to restore the fully sampled data with proper constraints. The state‐of‐the‐art method is to model the time‐domain data as the sum of exponential functions and reconstruct these data by enforcing the low rankness of Hankel matrix. However, this method is solved by minimizing the sum of singular values of the Hankel matrix, which leads to the distortion of low‐intensity spectral peaks. Here, a low rank Hankel matrix reconstruction approach with a partial sum of singular values is proposed to protect small singular values, which can faithfully reconstruct all peaks. Results on both synthetic and realistic NMR spectroscopy show that the proposed method can reconstruct a more consistent spectrum to the fully sampled one than other state‐of‐the‐art methods and have particular advantages on preserving low‐intensity peaks. |
| first_indexed | 2024-03-09T08:39:57Z |
| format | Article |
| id | doaj.art-6f8b142f64ed4280857246ab9df6c567 |
| institution | Directory Open Access Journal |
| issn | 1751-9675 1751-9683 |
| language | English |
| last_indexed | 2024-03-09T08:39:57Z |
| publishDate | 2021-02-01 |
| publisher | Hindawi-IET |
| record_format | Article |
| series | IET Signal Processing |
| spelling | doaj.art-6f8b142f64ed4280857246ab9df6c5672023-12-02T17:15:38ZengHindawi-IETIET Signal Processing1751-96751751-96832021-02-01151142710.1049/sil2.12010A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopyZhangren Tu0Zi Wang1Jiaying Zhan2Yihui Huang3Xiaofeng Du4Min Xiao5Xiaobo Qu6Di Guo7School of Computer and Information Engineering Xiamen University of Technology Xiamen People's Republic of ChinaDepartment of Electronic Science Xiamen University Xiamen People's Republic of ChinaSchool of Computer and Information Engineering Xiamen University of Technology Xiamen People's Republic of ChinaDepartment of Electronic Science Xiamen University Xiamen People's Republic of ChinaSchool of Computer and Information Engineering Xiamen University of Technology Xiamen People's Republic of ChinaSchool of Opto‐Electronic and Communication Engineering Xiamen University of Technology Xiamen People's Republic of ChinaDepartment of Electronic Science Xiamen University Xiamen People's Republic of ChinaSchool of Computer and Information Engineering Xiamen University of Technology Xiamen People's Republic of ChinaAbstract The nuclear magnetic resonance (NMR) spectroscopy has fruitful applications in chemistry, biology and life sciences, but suffers from long acquisition time. Non‐uniform sampling is a typical fast NMR method by undersampling the time‐domain data of the spectrum but need to restore the fully sampled data with proper constraints. The state‐of‐the‐art method is to model the time‐domain data as the sum of exponential functions and reconstruct these data by enforcing the low rankness of Hankel matrix. However, this method is solved by minimizing the sum of singular values of the Hankel matrix, which leads to the distortion of low‐intensity spectral peaks. Here, a low rank Hankel matrix reconstruction approach with a partial sum of singular values is proposed to protect small singular values, which can faithfully reconstruct all peaks. Results on both synthetic and realistic NMR spectroscopy show that the proposed method can reconstruct a more consistent spectrum to the fully sampled one than other state‐of‐the‐art methods and have particular advantages on preserving low‐intensity peaks.https://doi.org/10.1049/sil2.12010biomedical MRIHankel matricesimage reconstructionimage samplingmedical image processingNMR spectroscopy |
| spellingShingle | Zhangren Tu Zi Wang Jiaying Zhan Yihui Huang Xiaofeng Du Min Xiao Xiaobo Qu Di Guo A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy IET Signal Processing biomedical MRI Hankel matrices image reconstruction image sampling medical image processing NMR spectroscopy |
| title | A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy |
| title_full | A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy |
| title_fullStr | A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy |
| title_full_unstemmed | A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy |
| title_short | A partial sum of singular‐value‐based reconstruction method for non‐uniformly sampled NMR spectroscopy |
| title_sort | partial sum of singular value based reconstruction method for non uniformly sampled nmr spectroscopy |
| topic | biomedical MRI Hankel matrices image reconstruction image sampling medical image processing NMR spectroscopy |
| url | https://doi.org/10.1049/sil2.12010 |
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