Performance Analysis of Source Image Estimators in Blind Source Separation

TL;DR

This paper compares two widely used sensor response estimation methods in blind source separation, analyzing their differences, invariance properties, and performance through theory, perturbation analysis, and simulations.

Contribution

It provides the first detailed comparison of least-squares projection and inverse-based estimators in frequency-domain ICA, highlighting their conditions and differences.

Findings

Estimators are equivalent with orthogonal signal subspaces.

Differences are significant in non-orthogonal cases.

Simulations confirm theoretical insights.

Abstract

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.