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IMPROVED HARMONIC INCOMPATIBILITY REMOVAL FOR SUSCEPTIBILITY MAPPING VIA REDUCTION OF BASIS MISMATCH

Chenglong Bao1, Jianfeng Cai2, Jae Kyu Choi3, Bin Dong4, Ke Wei5   

  1. 1. Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China;
    2. Department of Mathematics, The Hong Kong University of Science and Technology, Hongkong, China;
    3. School of Mathematical Sciences, Tongji University, Shanghai 200092, China;
    4. Beijing International Center for Mathematical Research and Laboratory for Biomedical Image Analysis Beijing Institute of Big Data Research, Peking University, Beijing 100871, China;
    5. School of Data Science, Fudan University, Shanghai 200433, China
  • Received:2019-11-08 Revised:2020-04-18 Online:2022-11-15 Published:2022-11-18
  • Contact: Jae Kyu Choi, Email: jaycjk@tongji.edu.cn
  • Supported by:
    The research of the first author is supported in part by the NSFC Youth Program 11901338. The research of the second author is supported by the Hong Kong Research Grant Council (HKRGC) GRF 16306317 and 16309219. The research of the third author is supported by the NSFC Youth Program 11901436 and the Fundamental Research Program of Science and Technology Commission of Shanghai Municipality (20JC1413500). The research of the fourth author is supported by the NSFC grant 11831002. The research of the fifth author is supported by the National Natural Science Foundation of China Youth Program grant 11801088 and the Shanghai Sailing Program (18YF1401600).

Chenglong Bao, Jianfeng Cai, Jae Kyu Choi, Bin Dong, Ke Wei. IMPROVED HARMONIC INCOMPATIBILITY REMOVAL FOR SUSCEPTIBILITY MAPPING VIA REDUCTION OF BASIS MISMATCH[J]. Journal of Computational Mathematics, 2022, 40(6): 913-935.

In quantitative susceptibility mapping (QSM), the background field removal is an essential data acquisition step because it has a significant effect on the restoration quality by generating a harmonic incompatibility in the measured local field data. Even though the sparsity based first generation harmonic incompatibility removal (1GHIRE) model has achieved the performance gain over the traditional approaches, the 1GHIRE model has to be further improved as there is a basis mismatch underlying in numerically solving Poisson’s equation for the background removal. In this paper, we propose the second generation harmonic incompatibility removal (2GHIRE) model to reduce a basis mismatch, inspired by the balanced approach in the tight frame based image restoration. Experimental results shows the superiority of the proposed 2GHIRE model both in the restoration qualities and the computational efficiency.

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