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Sensors 2018, 18(12), 4260; https://doi.org/10.3390/s18124260

A Regularized Weighted Smoothed L0 Norm Minimization Method for Underdetermined Blind Source Separation

College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
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Received: 22 October 2018 / Revised: 28 November 2018 / Accepted: 30 November 2018 / Published: 4 December 2018
(This article belongs to the Special Issue Sensor Signal and Information Processing II)
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Abstract

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L 0 -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L p -RLSand achieves better performances when it is used for UBSS. View Full-Text
Keywords: image reconstruction; nullspace measurement matrix; regularized least squares problem; smoothed L0-norm; sparse signal recovery; UBSS; weighted function image reconstruction; nullspace measurement matrix; regularized least squares problem; smoothed L0-norm; sparse signal recovery; UBSS; weighted function
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Wang, L.; Yin, X.; Yue, H.; Xiang, J. A Regularized Weighted Smoothed L0 Norm Minimization Method for Underdetermined Blind Source Separation. Sensors 2018, 18, 4260.

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