Nonlinear thresholding of multiresolution decompositions adapted to the presence of discontinuities

Abstract

A new nonlinear representation of multiresolution decompositions and new thresholding adapted to the presence of discontinuities are presented and analyzed. They are based on a nonlinear modification of the multiresolution details coming from an initial (linear or nonlinear) scheme and on a data dependent thresholding. Stability results are derived. Numerical advantages are demonstrated on various numerical experiments.

A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

“…The starting point of this theory was Rahm's article (see [1]); a few years later several schemes were developed to extend the field of application to more complicated curves and surfaces. This theory has found huge success in many fields of application such as curve and surface reconstruction (see [2][3][4][5]), computer animation and graphics (see [6][7][8]), robotics (see [9]), medical science processing (see [10][11][12]), wavelet and frame construction (see [13][14][15][16]), etc. Subdivision schemes have a very strong link with splines, so they are widely used to describe various properties of splines such as shape reproduction and approximation order calculation [17][18][19].…”