Single-Trial Evoked Brain Responses Modeled by Multivariate Matching Pursuit

Abstract

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.

Multivariate Analysis of Single-Sweep Evoked Brain Potentials for Pharmaco-Electroencephalography

“…However, the use of MMP to decompose single-sweep EPs is not new and has previously been validated to extract meaningful information from EPs obtained during auditory stimuli [13]. Furthermore, matching pursuit has been used in several previous studies on average EPs in pharmaco-EEG [27], analysis of somatosensory EPs [28], investigation of the brain's pain processing [29] and preprocessing to source localization [30] and demonstrated a clear link between Gabor atoms and the corresponding EP components.…”

“…These features describe the morphology of the mean energy in all traces, which has advantages over alternative methods such as the wavelet transform. First, the decomposition is adapted to the dataset and hence only extracts features representing common waveforms reflecting pain-specific information [13]. Secondly, the decomposition does not require any a priori choice of the best matched filter for decomposition into a filter bank by either a finite impulse response filter or wavelet transform [32].…”

“…To adapt the feature extraction to reflect structures present in the actual data, Sieluzycki et al [13] used a multivariate matching pursuit (MMP) algorithm with a dictionary formed by Gabor atoms to detect common waveforms in all analysed sweeps. This approach successfully enabled an evaluation of the single-sweep amplitudes in the main peak across sweeps.…”

An Efficient Decoder for the Recognition of Event-Related Potentials in High-Density MEG Recordings

“…Certainly, the binary model reflects a quite naïve assumption, because we know that brain responses do not switch on and off but respond to events with bell-shaped deflections. In single trial analysis, typical ERP responses were shown to fit with Gabor functions [16]. Thus, to model a single ERP deflection, we define for the target event interval:…”

Quantifying the performance of compressive sensing on scalp EEG signals

“…Six different basis matrices Ψ are used in this work, each based on a different set of dictionary functions. Firstly the Gabor dictionary, as used in [8], [13], is used. Functions in this dictionary are defined by Gaussian envelope sinusoidal pulses:…”