(二)盲信号分离
接收信号为源信号的混合 问题: 如何从混合信号X(t)中恢复源信号S(t)？
从接收信号恢复源信号 Train W(t)
发现和创新 算法及其稳定性分析 在下述文章中， Tianping Chen Hong Chen, "Blind Extraction of Stochastic and Deterministic Signals by Neural Network Approach,“ 28th Asilomar Conference on Signals, Systems and Computers” Edited by Avtar Singh，IEEE Computer Society Press (1994) p. 892-896
信号盲分离神经网络算法 第一个对于两个信号源，设计了神经网络迭代算法解决信号盲分离问题 第一次给出了稳定性分析 为其它各种算法的稳定性分析提供了一个样板
发现和创新(1) 算法及其稳定性分析 给出了两个源信号分离的神经网络算法 Cichocki，et. al. 在Electronics Letters, 30, 1386-1387 1994）也讨论两个信号源的神经网络算法，但没有给出稳定性分析。过后，Deville, Y.在（Signal Processing, 51,229-233,1996），Macchi & Moreau,在（IEEE Transactions on Signal Processing Vol. 45, No. 4, pp.918-927，1997）分别讨论了上述同样算法的稳定性。
此文在Web of Science 记录中,至2000年 已被引用了43次. 被日本神经网络学会授予1997年度最佳论文奖。
1997年度日本神经网络学会论文奖
信号模拟 Matlab 中选取三个音频信号 采取不同方式混合 设计迭代神经网络算法 恢复出原信号
不可积盲信号分离算法 在文章 Shun-ichi Amari, Tianping Chen and Andrzej Cichocki. "Nonholonomic Orthogonal Learning Algorithms for Blind Source Separation" Neural Computation Vol. 12, (2000) pp. 1463-148
发现和创新(2) 不可积算法 提出了一种不可积 (Nonholonomic) 算法。 （训练权函数走的是不光滑的曲线）它可用来分离非平稳信号. 可讨论当信号源数目小于接收到信号数目时的分离问题。此时，逆阵 不存在。
源信号只有两个
A=[ 1.00000001 0.99999999 0.99999998 0.99999999 1.00000001 1.00000002 1.00000000 1.00000001 1.00000000] 混合矩阵严重病态
麦克风接收到三个几乎相同的信号
恢复出两个信号
IEEE Transactions on Signal Processing, 11(6),1490-1497, 2000 Interestingly, (12) belongs to a family of Blind source separation procedure in which a nonholonomic constrain is imposed on W(t) ([13]) 有意思的是, 算法(12) 属于一类带不可积(nonholonomic) 约束的盲信号分离算法. ([13]) 即我们的文章 其它引用文章就不再列出
在多本专著中被引用 Independent Component Analysis, A Volume in the Wiley Series on Adaptive Learning on Signal Processing Advances in Independent Component Analysis, Springer 2000 Unsupervised Adaptive Filtering, Vol. 1, A Volume in the Wiley Series on Adaptive Learning on Signal Processing… Unsupervised Adaptive Filtering, Vol. 2, A Volume in the Wiley Series on Adaptive Learning on Signal Processing
合作人：国际神经网络学会前主席，著名神经网络专家，日本RIKEN 脑科学研究所副所长Amari 教授的说明
This paper proposed a new learning algorithm, which works so well under fluctuating or temporally changing environments with a number of receiving signals being more than the number of source signals. Professor Chen first showed us by computer simulations how well the nonholonomic idea worked and gave the stability analysis. Then we collaborated for providing necessary mathematical foundation. This paper gives a rigorous mathematical analysis of the stability of the information-based gradient learning algorithm. The idea was closed related to Professor Chen’s previous paper (1994), in which the stability analysis for feedforward neural network approach was first given in detail in the case of two signals. In this paper, Professor Chen’s contribution is remarkable in the part of mathematical analysis….
Principal and minor components analyses are closely related problems, but their properties look quite different. We have unified the two in this paper for the first time. The idea was proposed by Professor Chen, and we collaborated for details of the mathematical proofs including the global stability analysis. This is continuation of the previous paper, and we gave more efficient and beautiful new algorithms. The idea was first proposed by Professor Chen and we collaborated for proving details.