Deconvolution of pulse trains with the L0 penalty

The output of many instruments can be modeled as a convolution of an impulse response and a series of sharp spikes. Deconvolution considers the inverse problem: estimate the input spike train from an observed (noisy) output signal. We approach this task as a linear inverse problem, solved using penalized regression. We propose the use of an L0penalty and compare it with the more common L2and L1penalties. In all cases a simple and iterative weighted regression procedure can be used. The model is extended with a smooth component to handle drifting baselines. Application to three different data sets shows excellent results.