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.

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Keywords Blind deconvolution, Ill-conditioned, Penalized regression, Spectra, Spike trains
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de Rooi, J.J, & Eilers, P.H.C. (2011). Deconvolution of pulse trains with the L0 penalty. Analytica Chimica Acta, 705(1-2), 218–226. doi:10.1016/j.aca.2011.05.030