Proposals for Performance Measurement in Source Separation

In this paper, we address a few issues related to the evaluation of the performance of source separation algorithms. We propose several measures of distortion that take into account the gain indeterminacies of BSS algorithms. The total distortion includes interference from the other sources as well as noise and algorithmic artifacts, and we define performance criteria that measure separately these contributions. The criteria are valid even in the case of correlated sources. When the sources are estimated from a degenerate set of mixtures by applying a demixing matrix, we prove that there are upper bounds on the achievable Source to Interference Ratio. We propose these bounds as benchmarks to assess how well a (linear or nonlinear) BSS algorithm performs on a set of degenerate mixtures. We demonstrate on an example how to use these figures of merit to evaluate and compare the performance of BSS algorithms.