  Objective: Cortico-muscular communication patterns are instrumental in
understanding movement control. Estimating significant causal relationships
between motor cortex electroencephalogram (EEG) and surface electromyogram
(sEMG) from concurrently active muscles presents a formidable challenge since
the relevant processes underlying muscle control are typically weak in
comparison to measurement noise and background activities. Methodology: In this
paper, a novel framework is proposed to simultaneously estimate the order of
the autoregressive model of cortico-muscular interactions along with the
parameters while enforcing stationarity condition in a convex program to ensure
global optimality. The proposed method is further extended to a non-convex
program to account for the presence of measurement noise in the recorded
signals by introducing a wavelet sparsity assumption on the excitation noise in
the model. Results: The proposed methodology is validated using both simulated
data and neurophysiological signals. In case of simulated data, the performance
of the proposed methods has been compared with the benchmark approaches in
terms of order identification, computational efficiency, and goodness of fit in
relation to various noise levels. In case of physiological signals our proposed
methods are compared against the state-of-the-art approaches in terms of the
ability to detect Granger causality. Significance: The proposed methods are
shown to be effective in handling stationarity and measurement noise
assumptions, revealing significant causal interactions from brain to muscles
and vice versa.
