We introduce a sliding window adaptive RLS-like algorithm for filtering alpha-stable noise. Unlike previously introduced stochastic gradient-type algorithms, the new adaptation algorithm minimizes the L/sub p/ norm of the error exactly in a sliding window of fixed size. Therefore, it behaves much like the RLS algorithm in terms of convergence speed and computational complexity compared to previously introduced stochastic gradient-based algorithms, which behave like the LMS algorithm. It is shown that the new algorithm achieves superior convergence rate at the expense of increased computational complexity.

In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.

We consider a wavelet-based edge preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e. edges in two dimensions or jumps in 1D). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the scale based structure of the underlying image. We demonstrate an efficient algorithm for obtaining the reconstructions from observed data and for choosing the multiple regularization parameters governing the priors.

A large class of physical phenomenon observed in practice exhibit non-Gaussian behavior. In this paper, /spl alpha/-stable distributions, which have heavier tails than Gaussian distribution, are considered to model non-Gaussian signals. Adaptive signal processing in the presence of such kind of noise is a requirement of many practical problems. Since, direct application of commonly used adaptation techniques fail in these applications, new approaches for adaptive filtering for /spl alpha/-stable random processes are introduced.