Blind source separation based on endpoint estimation with application to the MLSP 2006 data competition

The problem of blind source separation is usually solved by optimizing a contrast function that measures either the independence of several variables or the non-gaussianity of a single variable. If the problem involves bounded sources, this knowledge can be exploited and the solution can be found with a customized contrast that relies on a simple endpoint estimator. The minimization of the least absolute endpoint is closely related to and generalizes the minimization of the range, which has already been studied within the framework of blind source extraction. Using the least absolute endpoint rather than the range applies to a broader class of admissible sources, which includes sources that are bounded on a single side and, therefore, have an infinite range. This paper describes some properties of a contrast function based on endpoint estimation, such as the discriminacy. This property guarantees that each local minimum of the least absolute bound corresponds to the extraction of one source. An endpoint estimator is proposed, along with a specific deflation algorithm that is able to optimize it. This algorithm relies on a loose orthogonality constraint that reduces the accumulation of errors during the deflation process. This allows the algorithm to solve large-scale and ill-conditioned problems, such as those proposed in the MLSP 2006 data competition. Results show that the proposed algorithm outperforms more generic source separation algorithms like FastICA, as the sources involved in the contest are always bounded on at least one side.

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