Existence and identifiability of inverse solutions and estimation errors in cBSS for EMG

Establish the conditions under which inverse solutions exist and are identifiable in the convolutive blind source separation model for EMG-based motor neuron spike train identification, and quantify the associated estimation errors arising from imperfect inversion of motor unit action potentials, physiological and non-physiological noise, and ill-conditioning of the inverse problem.

Background

The cBSS framework underpins non-invasive identification of motor neuron activity from multichannel EMG, but practical ill-conditioning, non-unique MUAPs, and noise complicate inversion. While whitening and ICA-based objectives facilitate separation, theoretical guarantees regarding solution existence and identifiability—and systematic quantification of estimation errors—remain incomplete.

A rigorous characterization would inform algorithmic choices (e.g., objective functions, whitening strategies, extension factors) and provide bounds on performance and uncertainty, aiding translation to clinical contexts and other modalities such as ultrasound.