Performance Analysis of Source Image Estimators in Blind Source Separation
This work provides an incremental analysis for researchers in signal processing, clarifying the differences between two common estimators used to handle scaling ambiguity in blind source separation.
The paper analyzed two widely used methods for estimating sensor responses in blind source separation, specifically in Frequency-Domain Independent Component Analysis, to address scaling ambiguity, finding that they are equivalent only when signal subspaces are orthogonal and can yield substantially different results in some applications.
Blind methods often separate or identify signals or signal subspaces up to an unknown scaling factor. Sometimes it is necessary to cope with the scaling ambiguity, which can be done through reconstructing signals as they are received by sensors, because scales of the sensor responses (images) have known physical interpretations. In this paper, we analyze two approaches that are widely used for computing the sensor responses, especially, in Frequency-Domain Independent Component Analysis. One approach is the least-squares projection, while the other one assumes a regular mixing matrix and computes its inverse. Both estimators are invariant to the unknown scaling. Although frequently used, their differences were not studied yet. A goal of this work is to fill this gap. The estimators are compared through a theoretical study, perturbation analysis and simulations. We point to the fact that the estimators are equivalent when the separated signal subspaces are orthogonal, and vice versa. Two applications are shown, one of which demonstrates a case where the estimators yield substantially different results.