Bayesian methods for recursive estimation of partially observed non-Gaussian signals and images

Srinivas R Kadaba, Purdue University

Abstract

The goal of this research is to develop high performance recursive algorithms for estimation of non-Gaussian signals. In particular, we address the estimation of discrete and continuous-valued images from noisy observations and detection of digital data transmitted over wireless channels in the presence of multiple access interference. For images, the scene (uncorrupted image) and the noise in the observations are modeled as random processes. For image segmentation, the scene is modeled as a Markov Mesh Random field and the optimal recursive (but computationally complex) fixed-lag MAP estimator is derived first. Subsequently, hard and soft (conditional) decision feedback are introduced to reduce complexity. The resulting suboptimal algorithm is applied to several synthetic and real images. The results demonstrate its viability (both complexity-wise and performance-wise) and show its subjective relevance to the image segmentation problem. For image estimation, we fit non-Gaussian autoregressive (AR) models to the uncorrupted scene. We propose an algorithm to compute a fixed-lag near MMSE estimate of each pixel of the scene from the observations. We state and use a simple approximation which makes possible the development of a useful suboptimal nonlinear estimator called the Bayesian filter. A reduced-complexity version similar to the reduced-update Kalman filter is also proposed. Several examples demonstrate the non-Gaussian nature of residuals for AR image models and that our algorithm compares favorably with Kalman filtering techniques in such cases. For communications, we focus on interference suppression in time-division multiple access (TDMA) communications and describe a composite signal model consisting of the desired signal, interferer, channel parameters and noise. We then propose an optimal recursive algorithm which computes the the fixed-lag MAP estimate of each data symbol of the desired user (interferer symbols are treated as nuisance parameters) using the observations. The optimal algorithm is applied to typical scenarios specified in the North American IS-54 TDMA standard and results demonstrate the efficacy of our to interference cancellation. In particular, the capabilities of the algorithm are evidenced at moderate to low signal-to-interference ratios. The proposed algorithms are all derived in a common 1-step optimal framework with the imposition of the recursive constraint.

Degree

Ph.D.

Advisors

Gelfand, Purdue University.

Subject Area

Electrical engineering|Systems design|Statistics

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