The Separation of Independent Sources (SIS) is a challenging problem with significant potential applications. The problem is informally described as follows: several unknown but independent temporal signals propagate through a mixing and/or filtering, natural or synthetic, medium. By sensing outputs of this medium, a network (e.g., a neural network, a system, or a device) is configured to counteract the effect of the medium, and adaptively recovers the original, unmixed, signals. Only the property of signal independence is assumed for this processing. No additional apriori knowledge of the original signals is required. This processing represents a form of self (or unsupervised) learning. The weak assumptions and self-learning capability render such a network attractive from the viewpoint of real-world applications.
This neural network approach to the signal processing problem of SIS has great advantages over the existing adaptive filtering algorithms. For example when the mixture of other signals are labeled as noise in this approach, no specific apriori knowledge about any of the signals is assumed; only that the processed signals are independent. This is in contrast to the noise cancelation method, proposed by Widrow , which requires that a reference signal be correlated exclusively to the part of the waveform (i.e. noise) that needs to be filtered out. This latter requirement entails specific apriori knowledge about the noise as well as the signal(s).
The separation of independent sources is valuable in numerous and major applications in areas as diverse as telecommunication systems, sonar and radar systems, audio and acoustics, image/information processing, and biomedical engineering. Consider, e.g., the audio and sonar scenario when the original signals are sounds and the mixed signals are the output of several microphones or sensors placed at different vantage points. A network will receive, via each microphone, a mixture of sounds that are usually delayed relative to one another and/or the original sounds. The network's role is then to dynamically reproduce the original signals, where each separated signal can be subsequently channeled for further processing or transmission. Similar application scenarios can be described in situations involving heart-rate measurements, communication in noisy environments, engine diagnostics, and uncorrupted cellular phone communications.
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