Nonlinear Signal Processing

This book focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non-Gausssian, rather than Gaussian, processes. Notably, by concentrating on just two non-Gaussian models, a large set of tools is developed that encompass a large portion of the nonlinear signal processing tools proposed in the literature over the past several decades.

The chapters are grouped into three parts:

Part I provides the necessary theoretical tools that are used later in the text. These include a review of non-Gaussian models emphazing the class of generalized Gaussian distributions and the class of stable distributions. The basic principles of order statistics are coverd which are of essence in the study of weighted medians. Part I closes with a chapter on maximum likelihood and robust estimation principles which are used later in the book as the founation on which signal processing methods are built upon.

Part II comprises of three chapters focusing on signal processing tools developed under the generalized Gaussian model with an emphasis on the Laplacian model. Weighted medians, L-Filters, and several generalizations are studied at length.

Part III encompasses signal processing methods that emerge from parameter estimation within the stable distribution framework.