Evoked response denoising using nonlinear diffusion filtering of single-trial matrix representations

Recent progress in mathematical image processing shows a remarkable success when applying numerical methods to ill-posed partial differential equations (PDE). In particular, nonlinear diffusion filtering (NDF)process is an approach that belongs to such family of differential equations. It has been successfully applied in many recent methods for image processing and computer vision areas, particularly in denoising, smoothing, segmentation, and restoration. In this paper we focus on a novel NDF application, namely denoising of single-trials of auditory brainstem responses (ABRs) and the analysis of transcranial magnetic stimulation (TMS) responses.We show that by applying NDF on a matrix-form image of single-trials, we were able to denoise the single-trials, resulting in a better extraction of information over the ongoing experiment; morphology, eg. the latency of the single-trials according to different stimuli paradigms at different stimulation intensity levels. It is concluded that NDF represents a novel and useful approach for the analysis of single-trials in brain imaging.