This thesis considers new applications of non-Gaussian mixtures in the framework of statistical signal processing and pattern recognition. The non-Gaussian mixtures were implemented by mixtures of independent component analyzers (ICA). The fundamental hypothesis of ICA is that the observed signals can be expressed as a linear transformation of a set of hidden variables, usually referred to as sources, which are statistically independent. This independence allows factoring the original M-dimensional probability density function (PDF) of the data as a product of one-dimensional probability densities, greatly simplifying the modeling of the data. ICA mixture models (ICAMM) provide further flexibility by alleviating the independency requirement of ICA, thus allowing the model to obtain local projections of the data without compromising its generalization capabilities. Here are explored new possibilities of ICAMM for the purposes of estimation and classification of signals.The thesis makes several contributions to the research in non-Gaussian mixtures: (i) a method for maximum-likelihood estimation of missing data, based on the maximization of the PDF of the data given the ICAMM; (ii) a method for Bayesian estimation of missing data that minimizes the mean squared error and can obtain the confidence interval of the prediction; (iii) a generalization of the sequential dependence model for ICAMM to semi-supervised or supervised learning and multiple chains of dependence, thus allowing the use of multimodal data; and (iv) introduction of ICAMM in diverse novel applications, both for estimation and for classification.The developed methods were validated via an extensive number of simulations that covered multiple scenarios. These tested the sensitivity of the proposed methods with respect to the following parameters: number of values to estimate; kinds of source distributions; correspondence of the data with respect to the assumptions of the model; number of classes in the mixture model; and unsupervised, semi-supervised, and supervised learning. The performance of the proposed methods was evaluated using several figures of merit, and compared with the performance of multiple classical and state-of-the-art techniques for estimation and classification.Aside from the simulations, the methods were also tested on several sets of real data from different types: data from seismic exploration studies; ground penetrating radar surveys; and biomedical data. These data correspond to the following applications: reconstruction of damaged or missing data from ground-penetrating radar surveys of historical walls; reconstruction of damaged or missing data from a seismic exploration survey; reconstruction of artifacted or missing electroencephalographic (EEG) data; diagnosis of sleep disorders; modeling of the brain response during memory tasks; and exploration of EEG data from subjects performing a battery of neuropsychological tests. The obtained results demonstrate the capability of the proposed methods to work on problems wi...