eneral Approach to Blind Source Separation
Xi‐Ren Cao, Rueywen Liu · 1996
This paper identifies and studies two major issues in the blind source separation problem: separability and separation principles. We show that separability is an intrinsic property of the measured signals and can be described by the concept of m- row decomposability introduced in this paper; we also show that separation principles can be developed by using the structure characterization theory of random variables. In particular, we show that these principles can be derived concisely and intuitively by applying the DarmoisSkitovich theorem, which is well hown in statistical inference theory and psychology. Some new insights are gained for designing blind source separation illters. I. INTRODUCTION LIND SOURCE separation is a fundamental problem in signal processing. Consider a number of source signals coming from different sources and a number of receivers. Each receiver receives a linear combination of these source signals; combinations of these are called measured signals. Neither the structure of the linear combinations nor the source signals are known to the receivers. In this environment, we want to identify the linear combinations (blind identification problem) and decouple the linear combinations (blind source decoupling). This area has been very active, relevant works include (11-(31, (71-(10), and (12)-(21). Surprisingly, ths seemingly impossible problem has elegant solutions. It also has a broad range of applications in many areas, such as array signal processing 1141, seismic signal processing, identification of MA processing (15), and blind equalization (20). To distinguish the problem of source separation from that of signals separation (correlation in time domain is normally exploited in the latter but not in the former), the blind source separation problem is also called independent component anal- ysis (3). The goal of this problem is to design a filter, with the measured signals as its inputs, such that its output signals are as independent as possible. There are many works dealing with this subject (see, e.g., (11-131, 151, 1121, C131, 1151-(17), 1191). Our purpose is to provide a comprehensive study on the feasibility of decoupling and the basic principles for identification. We show that there are two major issues associated with this approach. First, it is possible to separate