Single-trial evoked brain responses modeled by multivariate matching pursuit

We present a new approach to the analysis of brain evoked electromagnetic potentials and fields. Multivariate version of the matching pursuit algorithm (MMP) performs an iterative, exhaustive search for waveforms, which optimally fit to signal structures, persistent in all the responses (trials) with the same time of occurrence, frequency, phase, and time width, but varying amplitude. The search is performed in a highly redundant time--frequency dictionary of Gabor functions, i.e., sines modulated by Gaussians. We present the feasibility of such a single-trial MMP analysis of the auditory M100 response, using an illustrative dataset acquired in a magnetoencephalographic (MEG) measurement with auditory stimulation with sinusoidal 1-kHz tones. We find that the morphology of the M100 estimate obtained from simple averaging of single trials can be very well explained by the average reconstruction with a few Gabor functions that parametrize those single trials. The M100 peak amplitude of single-trial reconstructions is observed to decrease with repetitions, which indicates habituation to the stimulus. This finding suggests that certain waveforms fitted by MMP could possibly be related to physiologically distinct components of evoked magnetic fields, which would allow tracing their dynamics on a single-trial level.