Estimating function approach to multichannel blind deconvolution

In this paper we study convergence and efficiency of the batch learning based on estimating functions for blind deconvolution. First the blind deconvolution problem is formulated in the framework of a semiparametric model, and a family of estimating functions is derived for blind deconvolution. Convergence rate of the batch estimator based on the estimating equation is then obtained. Superefficiency of the batch learning is proven in this framework.

[1]  Lang Tong,et al.  Indeterminacy and identifiability of blind identification , 1991 .

[2]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[3]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[4]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[5]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[6]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[7]  Yingbo Hua,et al.  Fast maximum likelihood for blind identification of multiple FIR channels , 1996, IEEE Trans. Signal Process..

[8]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[9]  Andrzej Cichocki,et al.  Robust neural networks with on-line learning for blind identification and blind separation of sources , 1996 .

[10]  Shun-ichi Amari,et al.  Blind source separation-semiparametric statistical approach , 1997, IEEE Trans. Signal Process..

[11]  S. Amari,et al.  Estimating Functions in Semiparametric Statistical Models , 1997 .

[12]  Shun-ichi Amari,et al.  Novel On-Line Adaptive Learning Algorithms for Blind Deconvolution Using the Natural Gradient Approach , 1997 .

[13]  S. Amari,et al.  Information geometry of estimating functions in semi-parametric statistical models , 1997 .

[14]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[15]  S. Amari,et al.  Geometrical structures of FIR manifold and their application to multichannel blind deconvolution , 1999, Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468).

[16]  Shun-ichi Amari,et al.  Superefficiency in blind source separation , 1999, IEEE Trans. Signal Process..