Expressions and Variants of the Linear-Quadratic Mixing Model

Abstract

This book deals with blind source separation and blind mixture identification methods intended for several classes of nonlinear mixtures, that is (1) mainly second-order mixtures (i.e., linear-quadratic mixtures, including their bilinear and purely quadratic restricted versions), and (2) to a much lower extent, higher-order polynomial mixtures. This chapter contains the definition of conventional linear (instantaneous, i.e., memoryless) mixtures and of their second-order extensions, including their above-mentioned general and restricted versions, as well as other specific versions. These models are first expressed in scalar form and then in matrix form. The reinterpretation of these nonlinear models as models that are linear with respect to an extended set of sources is discussed, together with the constraints which prevent one from processing these mixtures with standard methods intended for linear mixtures. The different aspects of the concept of determined mixtures, for these types of mixtures, are then analyzed.