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Sparse Bayesian learning approach for discrete signal reconstruction
Affiliation:1. College of Information Science and Technology, Donghua University, Shanghai 201620, China;2. Department of Electronic Engineering, Jiangsu University, Zhenjiang 212013, China;3. College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China;4. Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China;1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China;2. Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University, Ministry of Education, China;3. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China;1. Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong 510006 China;2. Department of Data Science, School of Internet Finance and Information Engineering, Guangdong University of Finance, Guangzhou, Guangdong 510521 China;3. College of Information Science and Technology, Donghua University, Shanghai 201620, China;1. College of Information Science and Technology, Donghua University, Shanghai 201620, China;2. Engineering Research Center of Digitalized Textile and Fashion Technology, Ministry of Education, Shanghai 201620, China;1. Zhengzhou University of Aeronautics, Zhengzhou, Henan 450046, China;2. School of Automation, Hubei University of Science and Technology, Xianning Avenue 88, Xianning, Hubei Province, 437100, P. R. China;1. University of California, Irvine, United States;2. City University of Hong Kong, City University of Hong Kong Shenzhen Research Institute, China;3. University of Miami, United States;4. Dalian University of Technology, China;5. Sun Yat-sen University, Guangxi Key Lab of Multi-source Information Mining & Security, China
Abstract:This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices.
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