A Primal Douglas–Rachford Splitting Method for the Constrained Minimization Problem in Compressive Sensing

Yu, Yongbin; Peng, Jigen; Han, Xuanli; Cui, Angang

doi:10.1007/s00034-017-0498-5

Cited by 9 publications

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“…where || • || F stands for the Frobenius norm. In order to emphasize the sparsity of the output weights, the L 1 norm is used to design the regularizer, i.e., ψ(V ) = ||V || 1 (34) According to (33) and (34), we specify (32) as follows:…”

Section: A Extreme Learning Machinementioning

confidence: 99%

“…In recent years, the sparsity regularization method has evoked the advancement of the imaging method, leading to much improvement in the accuracy of reconstruction. The L 1 norm based regularization (L1R) method is the most popular, and researchers have developed many excellent algorithms to solve it, e.g., the split Bregman technique [25] and the ADMM [26]- [28], the FIST algorithm [29], the forwardbackward splitting algorithm [30], [31], the primal-dual algorithm [32], the Douglas-Rachford splitting method [33], etc. The above-mentioned methods behave differently to diverse application scenarios.…”

Section: Introductionmentioning

confidence: 99%

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Prior Image Induced Regularization Method for Electrical Capacitance Tomography

2019

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The image reconstruction is a crucial step in the electrical capacitance tomography. This paper presents a new methodology for improving the reconstruction accuracy. The prior image induced regularization from the deep convolutional extreme learning machine (DCELM) is introduced, which is integrated with the domain knowledge related to imaging targets to form a more effective mathematical model for reconstruction. A new numerical scheme is developed to train the DCELM more effectively. The fast iterative shrinkage-thresholding method is embedded into the alternating direction method of multipliers (ADMM) to form a new solver for the proposed imaging model. Extensive validations are implemented to evaluate the proposed imaging method. The numerical results demonstrate that the proposed imaging technique outperforms the state-of-the-art reconstruction methods and produces better reconstructions. INDEX TERMS Prior image induced regularization, image reconstruction, inverse problem, deep convolutional extreme learning machine, iterative imaging method, electrical capacitance tomography. QIBIN LIU received the B.Eng. and M.Sc. degrees in engineering thermophysics from Xi'an Jiaotong University, China, in 2002 and 2005, respectively, and the Ph.D. degree in engineering thermophysics from the Institute of Engineering Thermophysics, Chinese Academy of Sciences, China, in 2008. He is currently a Professor with the Institute of Engineering Thermophysics, Chinese Academy of Sciences, China. He has published more than 80 research papers. His research interests include solar energy utilization technologies, energy system integration, electrical capacitance tomography, inverse problems in engineering and science, and computational fluid dynamics.

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Section: A Extreme Learning Machinementioning

confidence: 99%