Deconvolution of sparse positive spikes
- Details
- Publication Year 2004-12,Volume 13,Issue #4,Page 853-870
- Journal Title
- JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
- Publication Type
- Journal Article
- 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 oil 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 fitted values. In the latter case. we point out that in the context of deconvolution and the general linear inverse problems with positivity constraints, a counterpart of the EM algorithm exists for the problem of minimizing, the Kullback-Leibler divergence. We graphically compare the performance of these deconvolvers using data simulated from a spike-convolution model and DNA sequencing data.
- Publisher
- AMER STATISTICAL ASSOC
- Keywords
- PARAMETRIC DECONVOLUTION; MAXIMUM-LIKELIHOOD; EM ALGORITHM; CONVERGENCE; REGRESSION
- Publisher's Version
- https://doi.org/10.1198/106186004X13118
- Terms of Use/Rights Notice
- Refer to copyright notice on published article.
Creation Date: 2004-12-01 12:00:00