Faculty Bibliography

This paper describes a new wavelet-based denoising algorithm based on a non-stationary noise assumption. Even though stationary noise models can simplify the development and implementation of denoising algorithms, they do not always accurately describe the statistical properties of the noise. The proposed algorithm has been developed to address signal processing problems under environments where the noise is spatially varying. We illustrate two signal denoising examples in order to show the performance of the proposed algorithm.

The most important technical limitation affecting dynamic measurements with PET is low signal-to-noise ratio (SNR). Several reports have suggested that wavelet processing of receptor kinetic data in the human brain can improve the SNR of parametric images of binding potential (BP). However, it is difficult to fully assess these reports because objective standards have not been developed to measure the tradeoff between accuracy (e.g. degradation of resolution) and precision. This paper employs a realistic simulation method that includes all major elements affecting image formation. The simulation was used to derive an ensemble of dynamic PET ligand (11C-raclopride) experiments that was subjected to wavelet processing. A method for optimizing wavelet denoising is presented and used to analyze the simulated experiments. Using optimized wavelet denoising, SNR of the four-dimensional PET data increased by about a factor of two and SNR of three-dimensional BP maps increased by about a factor of 1.5. Analysis of the difference between the processed and unprocessed means for the 4D concentration data showed that more than 80% of voxels in the ensemble mean of the wavelet processed data deviated by less than 3%. These results show that a 1.5x increase in SNR can be achieved with little degradation of resolution. This corresponds to injecting about twice the radioactivity, a maneuver that is not possible in human studies without saturating the PET camera and/or exposing the subject to more than permitted radioactivity.

BACKGROUND: Power in the gamma band EEG increases during saccades in normal subjects. OBJECTIVE: To develop a potential method to quantify signs of cortical responsiveness in persistent vegetative state (PVS) we quantified gamma range EEG in association with conjugate slow ballistic eye movements (SBEM). METHODS: The EEG and the simultaneous electro-oculogram were recorded in 14 (8F/6M) PVS patients. Clinical scoring was based on the Glasgow Coma Scale (GCS) and Coma Rating Scale (CRS). The Wavelet Transform, followed by Hilbert transform was applied to the EEG and gamma power distribution was quantified relative to the timing of an eye movement. We correlated the clinical and the neurophysiological measures. RESULTS: Gamma activity was present in all PVS patients. Its power was modulated in association with eye movements only in less severely affected patients, with minimum power prior to, and maximum power during the eye movement. In severely affected patients there was no evidence of a temporal relationship between gamma power and the phase of the eye movement. CONCLUSIONS: Detecting changes in the time course of gamma power in relation to conjugate ballistic eye movements provides a quantitative neurophysiological method for prospective longitudinal studies to explore if the preservation of this CNS function relates to the potential for recovery in PVS patients.

In this paper we introduce a class of multivariate quasi-Laplacian models as a generalization of the single-variable Laplacian distribution to multi-dimensions. A mixture model is used as the wavelet coefficient prior for the wavelet-based Bayesian image denoising algorithm. As a multivariate probability model, it is able to capture the intra-scale or inter-scale dependencies among wavelet coefficients. Two special cases are studied for orthogonal transform based image denoising. Efficient parameter estimation methods and denoising rules are derived for the two cases. Denoising results are compared with existing techniques in both PSNR values and visual qualities.

Wavelet domain statistical modeling of images has focused on modeling the peaked heavy-tailed behavior of the marginal distribution and on modeling the dependencies between coefficients that are adjacent (in location and/or scale). In this paper we describe the extension of the Laplace marginal model to the multivariate case so that groups of wavelet coefficients can be modeled together using Laplace marginal models. We derive the nonlinear MAP and MMSE shrinkage functions for a Laplace vector in Gaussian noise and provide computationally efficient approximations to them. The development depends on the generalized incomplete Gamma function.