Journal article

Deconvolution of sparse positive spikes

LM Li, TP Speed

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS | AMER STATISTICAL ASSOC | Published : 2004

Abstract

Deconvolution is usually regarded as one of the ill-posed problems in applied mathematics if no constraints on the unknowns are assumed. This article discusses the idea of well-defined statistical models being a counterpart of the notion of well-posedness. We show that constraints on the unknowns such as positivity and sparsity can go a long way towards overcoming the ill-posedness in deconvolution. We show how these issues are dealt with in a parametric deconvolution model introduced recently. From the same perspective we take a fresh look at two familiar deconvolvers: the widely used Jansson method and another one that minimizes the Kullback-Leibler divergence between observations and fitt..

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University of Melbourne Researchers