TY - GEN
T1 - A Convergence and Asymptotic Analysis of Nonlinear Separation Model
AU - Wang, Lu
AU - Ohtsuki, Tomoaki
PY - 2019/3/4
Y1 - 2019/3/4
N2 - Nonlinear blind source separation is the process of estimating either the original signals or mixture functions from the degraded signals, without any prior information about original sources. The key idea is to recover the sources by estimating an approximation function so as to approximate the inverse of mixing function. However, in practice, the approximation function is derived from some estimation algorithm with finite sample size, which leads to the performance loss. In this paper, we work on the convergence and asymptotic analysis of the separation approach, which uses the flexible approximation to extract the nonlinearity of mixture function so that to make the problem linearly separable. The analysis stems from the performance of a mismatched estimator that accesses the finite sample size. By providing a closed-form expression of normalized mean squared error (NMSE), we can present a novel algebraic formalization that leads to the upper bound on the estimation error. The simulation results show that if the flexible approximation can extract the nonlinearity of mixing functions, the minimized NMSE can be achieved as the sample size tends to be infinity. This implies that the algorithm is feasible to separate the distortion of the nonlinear mixture.
AB - Nonlinear blind source separation is the process of estimating either the original signals or mixture functions from the degraded signals, without any prior information about original sources. The key idea is to recover the sources by estimating an approximation function so as to approximate the inverse of mixing function. However, in practice, the approximation function is derived from some estimation algorithm with finite sample size, which leads to the performance loss. In this paper, we work on the convergence and asymptotic analysis of the separation approach, which uses the flexible approximation to extract the nonlinearity of mixture function so that to make the problem linearly separable. The analysis stems from the performance of a mismatched estimator that accesses the finite sample size. By providing a closed-form expression of normalized mean squared error (NMSE), we can present a novel algebraic formalization that leads to the upper bound on the estimation error. The simulation results show that if the flexible approximation can extract the nonlinearity of mixing functions, the minimized NMSE can be achieved as the sample size tends to be infinity. This implies that the algorithm is feasible to separate the distortion of the nonlinear mixture.
UR - http://www.scopus.com/inward/record.url?scp=85063487874&partnerID=8YFLogxK
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U2 - 10.23919/APSIPA.2018.8659740
DO - 10.23919/APSIPA.2018.8659740
M3 - Conference contribution
AN - SCOPUS:85063487874
T3 - 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings
SP - 963
EP - 971
BT - 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018
Y2 - 12 November 2018 through 15 November 2018
ER -