Neurobiologists recently developed tools to record from large populations of neurons, and early results suggest that neurons interact to encode information jointly. However, traditional statistical analysis techniques are inadequate to elucidate these interactions. This thesis develops two multivariate statistical dependence measures that, unlike ...

In this thesis, we consider wavelet-based denoising of signals and images contaminated with white Gaussian noise. Existing wavelet-based denoising methods are limited because they make at least one of the following three unrealistic assumptions: (1) the wavelet coefficients are independent, (2) the signal component of the wavelet coefficient distribution ...

Classical Gaussian, Markov, and Poisson models have played a vital role in the remarkable success of statistical signal processing. However, a host of signals---images, network traffic, financial times series, seismic measurements, wind turbulence, and others---exhibit properties beyond the scope of classical models, properties that are crucial to ...

Prediction of future time-series values, based on a finite set of available observations, is a prevalent problem in many branches of science and engineering. By making the assumption that the time series is either Gaussian or linear, the classical technique of linear prediction may be fruitfully applied. Unfortunately, few, if any, real-world time ...

Analytic solutions to determining the optimal set of system parameters and the associated performance of random input systems are typically intractable. One often only has access to the system's output under a variety of inputs, thereby requiring the optimization routine to be insensitive to the noise inherent in estimating the performance. The well ...

In this thesis, the method of "classification with empirically observed statistics"--also known as empirical classification, empirical detection, universal classification, and type-based detection--is configured and applied to the despreading/detection receiver operation of a spread-spectrum (SS), code division multiple access (CDMA) communications ...

Despite their success in other areas of statistical signal processing, current wavelet-based image models are inadequate for modeling patterns in images, due to the presence of unknown transformations inherent in most pattern observations. In this thesis we introduce a hierarchical wavelet-based framework for modeling patterns in digital images. This ...

This thesis proposes a new approach to wavelet-based image deconvolution that comprises Fourier-domain system inversion followed by wavelet-domain noise suppression. In contrast to other wavelet-based deconvolution approaches, the algorithm employs a regularized inverse filter, which allows it to operate even when the system is non-invertible. Using ...

Codelength based inference is used to decode binary symbols distorted by an inter-symbol interference (ISI) channel with additive noise. The transmitted signals are antipodal waveforms constructed from $\pm$1 valued signature sequences. The receiver adapts to the unknown channel by training on a known preamble sequence. The training sequence is ...

Analytical solutions of the performance of optical communication systems are difficult to obtain and often, Monte Carlo simulations are used to achieve realistic estimates of the performance of such systems. However, for high performance systems, this technique requires a large number of simulation trials for the estimates to be in a reasonable ...