Model Selection and Sparse Modeling
Abstract: Parametric signal models are used in a multitude of signal processing applications. This thesis deals with signals for which there are many candidate models, and it is not a priori known which model is the most appropriate one. The first part of the thesis treats cases for which the set of models is relatively small, so that it is possible to evaluate each model in the set separately. The second part deals with sparse models, i.e., models sharing the same parameter vector, but for which any combination of zero valued and non-zero valued parameters is possible. Sparse models appear in a variety of applications, such as statistical data analysis, communications, and active sensing, such as radar and non-destructive testing.An important problem considered in the two parts of the thesis is that of model selection, i.e., how to select the most appropriate model (according to some criterion) from the set of candidates. To this end, both the classical information criterion (IC) approaches, such as AIC, BIC and GIC, as well as maximum a posteriori probability based methods derived in the Bayesian framework are used.Finally, the task of symbol detection for applications in communications is considered. The maximum a posteriori probability symbol detector is derived for a few different channel models.
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