Faculty Bibliography

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.

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.

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.

This paper introduces an anisotropic decomposition structure of a recently introduced 3-D dual-tree discrete wavelet transform (DDWT), and explores the applications for video denoising and coding. The 3-D DDWT is an attractive video representation because it isolates motion along different directions in separate subbands, and thus leads to sparse video decompositions. Our previous investigation shows that the 3-D DDWT, compared to the standard discrete wavelet transform (DWT), complies better with the statistical models based on sparse presumptions, and gives better visual and numerical results when used for statistical denoising algorithms. Our research on video compression also shows that even with 4:1 redundancy, the 3-D DDWT needs fewer coefficients to achieve the same coding quality (in PSNR) by applying the iterative projection-based noise shaping scheme proposed by Kingsbury. The proposed anisotropic DDWT extends the superiority of isotropic DDWT with more directional subbands without adding to the redundancy. Unlike the original 3-D DDWT which applies dyadic decomposition along all three directions and produces isotropic frequency spacing, it has a non-uniform tiling of the frequency space. By applying this structure, we can improve the denoising results, and the number of significant coefficients can be reduced further, which is beneficial for video coding.