盲訊號分離 (i.e, 給定 「觀測訊號」, 分離出獨立的 「原始訊號」) 是通訊, 電機, 生醫等領域的重要課題。 常用來解釋盲訊號分離的實例是所謂的雞尾酒宴會問題: 將雞尾酒宴會中兩個麥克風收到的觀測訊號, 分離出會場中的原始訊號 (假設原始訊號為講者訊號與其他雜訊, 且兩者獨立) 。 過去文獻在探討 「盲訊號分離」 問題時, 常用的演算法是「獨立成份分析」 (Independent Component Analysis, ICA) 。 具我們所知, 傳統 ICA 演算法的目標函數是藉著原始訊號的非高斯性以達到獨立性。
本論文探討盲訊號分離問題, 所提出的方法稱為 MIK-ICA, 其中 MIK 為 Mean Inequality and Kernel density estimation 之三個關鍵字的縮寫。 本文所提出的 MIK-ICA 著眼於直接以統計獨立為目標, 結合平均數不等式與核密度估計, 達到準確估計出原始訊號之目的。 文中以週期訊號混和雜訊, 以及人體脈波訊號混和雜訊之實驗, 來證實所提出的 MIC-ICA 與傳統 ICA 的方法是可行的。

“Blind Source Separation (BSS)” (i.e, Estimating independent source signals based on observed signals) problems can be found in many areas, such as communication, electrical engineering, and biomedical engineering. A famous example of BSS is the so-called “cocktail party problem”; in a cocktail party, we want to separate the source signals (e.g., speech and other noises) based on the observed
signals collected by two microphones. Independent Component Analysis (ICA) is the most commonly used approach for the BSS problem. The objective function used in the traditional ICA algorithm is measured by non-gaussianity of observed signals.
We propose a new ICA algorithm, named the MIK-ICA. MIK captures 3 key words: Mean-Inequality and Kernel-Density-Estimation. The objective function used in the proposed MIK-ICA is statistical independence, in which we combine mean-inequality and kernel density estimation techniques. Experimental results show that the proposed MIK-ICA works as well as many traditional ICA algorithms to separate studied simulated signals from noises and to separate studied pulse signals from noises.

[1] Wei Li, “Blind Signal Separation with Kernel Probability Density Estimation
Based on MMI Criterion Optimized by Conjugate Gradient”, Journal of
Communications Vol. 9, No. 7, (2014).
[2] Daniel J. Hendersona and Christopher F. Parmeter, “Normal reference bandwidths
for the general order, multivariate kernel density derivative estimator”
Journal of Statistics and Probability Letters Vol. 82, No. 12, pp.
2198-2205, (2012).
[3] M. M. Mena and B. Mandersson, “Analysis of The Vascular Sounds of The
Arteriovenous Fistula’s Anastomosi”, 33rd Annual International Conference
of the IEEE EMBS, pp. 3784-3787, (2011).
[4] J.E. Chac`on and T. Duong, “Multivariate plug-in bandwidth selection with
unconstrained pilot bandwidth matrices”, Journal of TEST, , Vol. 19, No.
2, pp. 375-398. (2010).
[5] P. S. Bullen, “Handbook of Means and Their Inequalities”, Springer Science+
Business Media, Berlin, New York. 2nd ed. (2003).
[6] Duong, Tarn, and Martin Hazelton. “Plug-in bandwidth matrices for bivariate
kernel density estimation.” Journal of Nonparametric Statistics 15.1 pp.17-
30, (2003)
[7] Venables, W. N. and Ripley, B. D. Modern Applied Statistics with S. Fourth
edition. Springer. (2002)
[8] K. Parsopoulos, M. Vrahatis, “Recent approaches to global optimization problems
through particle swarm optimization”, Natural Computing, Vol. 1, pp.
235-306, (2002).
[9] A. Hyv¨arinen and E. Oja, Independent Component Analysis, Vol. 46. John
Wiley & Sons, (2004).
[10] Cardoso, J-F. “Blind signal separation: statistical principles.”, Proceedings
of the IEEE 86. 10. pp. 2009-2025. (1998).
[11] Shannon, Claude E. “A mathematical theory of communication”, ACM
SIGMOBILE Mobile Computing and Communications Review 5.1. pp. 3-
55. (2001).
[12]Silverman, Bernard W. Density estimation for statistics and data analysis,
Vol. 26. CRC press, (1986).
[13]Broyden, Charles George “The convergence of a class of double-rank minimization
algorithms.” IMA Journal of Applied Mathematics 6.1 (1970).
[14]https://commons.wikimedia.org/wiki/File:Synthetic data 2D KDE.png
[15]江秀月, “創新的方法應用於廔管裝設與血管狹窄的血管音研究” 清華大學工業工
程與工程管理學系工程碩士在職專班學位論文(2013).
[16]陳則丞,“以獨立成分分析為基之支援向量迴歸模式預測時間系列股價”, 中山大學
資訊管理學系研究所學位論文(2012).
[17]趙昶凱, “新穎獨立成份分析應用於雜訊語音辨識”, 成功大學資訊工程學系研究所
學位論文(2007).
[18]桑慧敏, 機率與推論統計原理, McGraw-Hill International. (第一版), (2007).