A Two-Stage Separation Algorithm for Weak Correlation Source Signals
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A Two‑Stage Separation Algorithm for Weak Correlation Source Signals Tiaojun Zeng1 · Changzheng Liu1 Accepted: 11 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we propose a separation algorithm for weakly correlated source signals. At present, there are many blind source separation algorithms based on independent component analysis, which can only deal with the separation of uncorrelated source signals. However, the assumption that the source signals are independent is too strict in practical application, so the application of the separation algorithm is limited. The proposed weak correlation source signal separation algorithm is divided into two stages. In the first stage, the correlation matrices of mixed signals are first decomposed into two parts, and then their image matrices are introduced. Finally, the objective function is constructed. Using the iterative algorithm to compute this function, we prove that when the function tends to zero, similar matrices of independent parts of the aforementioned correlation matrices are obtained. In the second stage, the joint diagonal matrix model is established by using these similarity matrices, and finally the separable separation matrix is obtained by optimizing the model so as to achieve the purpose of separating the source signals. Simulation experiments also verify the effectiveness of the algorithm. Keywords Blind signal separation · Two-stage separation algorithm · Weakly correlated source signals · Independent component analysis
1 Introduction Blind source separation (BSS) refers to the restoration of the original signal source from the mixed signal when the signal or the information of the mixing process is weak or unavailable [1]. It originated from the well-known ’Cocktail Party’ problem in the field of speech signal processing. The core of the problem is how to separate mixed speech signals [2]. However, with the development of BSS technology, BSS is no longer limited to speech signal processing, and has shown great application prospects in the fields of biomedical signal processing, geological prospecting, image processing, sonar and radar signal detection, and communication signal processing, etc.[3–7]. * Changzheng Liu [email protected] 1
School of Information Science and Technology, Shihezi University, Shihezi 610031, Xinjiang, China
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T. Zeng, C. Liu
The problem of blind source separation is mainly solved by independent component analysis (ICA) [8–10], which assumes that the original signal sources are statistically independent of each other. ICA has become the most popular method of blind source separation due to the applicability of the independence assumption in a wide range of applications and the mathematical processability of the corresponding framework. Under different data model assumptions, such as the time structure, sparsity and special constant modulus or finite letter structure of communication signals, many other blind source separation methods ha
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