Parametric deconvolution of positive spike trains

Abstract

This paper describes a parametric deconvolution method (PDPS) appropriate for a particular class of signals which we call spike-convolution models. These models arise when a sparse spike train-Dirac deltas according to our mathematical treatment-is convolved with a fixed point-spread function, and additive noise or measurement error is superimposed. We view deconvolution as an estimation problem, regarding the locations and heights of the underlying spikes, as well as the baseline and the measurement error variance as unknown parameters. Our estimation scheme consists of two parts: model fitting and model selection. To fit a spike- convolution model of a specific order, we estimate peak loca..