A Framework for Non-Gaussian Signal Modeling and Estimation
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
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This thesis develops a new statistical framework for analyzing and processing stationary non-Gaussian signals. The proposed framework consists of a collection of mathematical techniques for modeling such signals as well as an associated collection of model-based algorithms for solving certain basic signal processing problems. Two inference problems commonly encountered in practice are given special consideration i identification of the parameter values of a non-Gaussian signal source based on a clean observation of the source output and ii recovery of the source output itself based on a noisy observation and complete knowledge of the measurement model. These problems are referred to, respectively, as source identification and signal estimation. Two probabilistic signal models are considered. The first, which is termed the ARGMIX signal model, is a direct generalization of the classical autoregressive AR linear-Gaussian model. Under the ARGMIX model, a signal is characterized as the output of an AR linear time-invariant LTI system driven by a noise process whose samples are independent and identically distributed according to a Gaussian-mixture GMIX density, rather than a purely Gaussian density. For this model, the source identification problem can be solved efficiently with an iterative technique designed to estimate the AR parameters of the LTI system as well as the means, variances, and weighting coefficients of the GMIX density However, the problem of optimally estimating an ARGMIX signal in independent additive noise is shown to require a number of computations growing exponentially with the number of samples contained in the observation. For the signal estimation problem, therefore, only approximate suboptimal algorithms are proposed. A second signal model is introduced as a way of overcoming the computational complexity of the ARGMIX structure.
- Numerical Mathematics
- Statistics and Probability