Faculty Bibliography

The problem of image denoising has received more attention than the problem of image sharpening. In the paper, we propose that wavelet-based algorithms for image denoising can be used to perform image sharpening. Consequently, a variety of new image sharpening techniques becomes available. We examine the sharpening of natural images using an algorithm for image denoising with oriented complex 2D wavelets.

It is well documented that the statistical distribution of wavelet coefficients for natural images is non-Gaussian and that neighboring coefficients are highly dependent. In this paper, we propose a new multivariate non-Gaussian probability model to capture the dependencies among neighboring wavelet coefficients in the same scale. The model can be expressed as K exp(-parallel towparallel to) where w is an N-element vector of wavelet coefficients and parallel towparallel to is a convex combination of l(2) norms over subspaces of R-N. This model includes the commonly used independent Laplacian model as a special case but it has many more degrees of freedom. Based on this model, the corresponding non-linear threshold (shrinkage) function for denoising is derived using Bayesian estimation theory. Although this function does not have a closed-form solution, a successive substitution method can be used to numerically compute it.

Complex discrete wavelet transforms (DWT) have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex DWT. (C) 2003 Elsevier Science B.V. All rights reserved.

Connexions is a new approach to authoring, teaching, and learning that aims to fully exploit modem information technology. Available free of charge to anyone under open-content and open-source licenses, Connexions offers custom-tailored, current course material, is adaptable to a wide range of learning styles, and encourages students to explore the links among courses and disciplines. In contrast to the traditional process of textbook writing and publishing, Connexions fosters world-wide, cross-institution communities of authors, instructors, and students, who collaboratively and dynamically fashion "modules" from which courses are constructed. We believe the ideas and philosophy embodied by Connexions have the potential to change the very nature of textbook writing and publishing, producing a dynamic, interconnected educational environment that is pedagogically sound, both time and cost efficient, and fun. This paper overviews the philosophy and technology behind Connexions and describes a nascent community developing material for DSP education.

This paper describes the design of type III and type IV linear-phase finite-impulse response (FIR) low-pass digital differentiators according to the maximally flat criterion. We introduce a two-term recursive formula that enables the simple stable computation of the impulse response coefficients. The same recursive formula is valid for both Type III and Type IV solutions.