Basarab Matei

Quasilinear subdivision schemes with applications to ENO interpolation

Abstract We analyze the convergence and smoothness of certain class of nonlinear subdivision schemes. We study the stability properties of these schemes and apply this analysis to the specific class based on ENO and weighted-ENO interpolation techniques. Our interest in these techniques is motivated by their application to signal and image processing.

Compact representation of images by edge adapted multiscale transforms

We introduce new multiscale representations for images which incorporate a specific geometric treatment of edges. The associated transforms are inherently nonlinear and nontensor product, in contrast to classical wavelet basis decompositions over which they exhibit visual improvement in terms of compression. This approach can be viewed as a bridge between edge detection and the nonlinear multiresolution representations of Ami Harten (see Journal of Applied Numerical Mathematics, vol.12, p.153-93, 1993).

Nonlinear Subdivision Schemes: Applications to Image Processing

In classical subdivision schemes, some initial discrete data set v 0 is refined iteratively, following a prescribed linear rule which is summarized by n n

Edge adapted nonlinear multiscale transforms for compact image representation

{v^j} = S{v^{j - 1}} = cdots = {S^j}{v^0}

Full length article: Smoothness characterization and stability of nonlinear and non-separable multiscale representations

n nwhere v j are the numerical data at resolution 2-j and S the subdivision operator. One is usually interested in the convergence properties of this process to some limit function f = S ∞ v 0. In the simplest setting the data v j belongs to the uniform grid 2-j ℤ and convergence means that sup k n n

Nonlinear and Nonseparable Bidimensional Multiscale Representation Based on Cell-Average Representation

left| {f({2^{ - j}}k) - v_k^j} right|