Scale-Invariant Reconstruction of Source Images in Blind Source Separation

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, each of which provides an estimator that is invariant to the unknown scaling. One approach is the least-squares projection, while the other one assumes a regular mixing matrix and computes its inverse. We compare the estimators through a theoretical study, perturbation analysis and simulations, and show some applications.