In this paper we present general algebraic approach to an Extended Dynamic Independent Component Analysis (EDICA) for multichannel blind signal separation/deconvolution. Precise algebraic equivalence and direct analogies between instantaneous blind source separation (BSS) and dispersive (dynamic) blind signal separation/deconvolution (referred also as multichannel blind deconvolution - (MBD)) problems are shown, as well as, the equivalence of the problem in time domain and the Z-transform domain. For circular convolution the equivalence (analogy) is precise for finite length time series, while for linear convolution such analogy is valid only in asymptotic sense for infinite length series. Elegant and concise derivation of learning algorithms in the time domain is presented using the algebraic properties of the convolution operator and relationships between convolution and cross-correlation. Using this general concept un-supervised learning algorithms (both batch and on-line algorithms) are developed for multichannel blind deconvolution/separation problems. Computer simulation experiments confirm validity and high performance of the proposed algorithms. The proposed approach and some automatic rules can be applied not only to the known, already existing algorithms for blind separation and extraction of sources but we hope could be also used for extension and generalization of learning rules developed in future.
|Number of pages||6|
|Publication status||Published - 1998|
|Event||Proceedings of the 1998 IEEE International Joint Conference on Neural Networks. Part 1 (of 3) - Anchorage, AK, USA|
Duration: 4 May 1998 → 9 May 1998
|Conference||Proceedings of the 1998 IEEE International Joint Conference on Neural Networks. Part 1 (of 3)|
|City||Anchorage, AK, USA|
|Period||4/05/98 → 9/05/98|