Journal ArticleDOI
Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing
TLDR
A nonlinear multiresolution scheme within Harten's framework is presented, based on a new nonlinear, centered piecewise polynomial interpolation technique, which shows promising results in terms of convergence, smoothness, and stability.Abstract:
A nonlinear multiresolution scheme within Harten's framework is presented, based on a new nonlinear, centered piecewise polynomial interpolation technique. Analytical properties of the resulting subdivision scheme, such as convergence, smoothness, and stability, are studied. The stability and the compression properties of the associated multiresolution transform are demonstrated on several numerical experiments on images.read more
Citations
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Journal ArticleDOI
Stability of Nonlinear Subdivision and Multiscale Transforms
Stanislav Harizanov,Peter Oswald +1 more
TL;DR: In this paper, a new general sufficient condition for the Lipschitz stability of nonlinear subdivision schemes and multiscale transforms in the univariate case is presented, which covers the special cases (weighted essentially nonoscillatory scheme, piecewise polynomial harmonic transform) considered so far but also implies the stability in some new cases (median interpolating transform, power-p schemes, etc.).
Journal ArticleDOI
Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms
TL;DR: This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms and shows that if some contractivity properties are satisfied, then stability and convergence can be achieved.
Journal ArticleDOI
Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications
TL;DR: A generalized k-step iterative application of Newton's method with frozen derivative is studied and used to solve a system of nonlinear equations and the maximum computational efficiency is computed.
Journal ArticleDOI
Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators
TL;DR: A new approach is introduced based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction.
Journal ArticleDOI
Nonlinear Harten's multiresolution on the quincunx pyramid
TL;DR: This paper links the nonseparable quincunx pyramid and the nonlinear discrete Harten's multiresolution framework and proposes and tests a nonlinear reconstruction of these representations.
References
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Journal ArticleDOI
Uniformly high order accurate essentially non-oscillatory schemes, 111
TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
Book ChapterDOI
Symmetric Iterative Interpolation Processes
Gilles Deslauriers,Serge Dubuc +1 more
TL;DR: In this paper, a symmetric iterative interpolation process is defined using a base b and an even number of knots, and the main properties of this process come from an associated function F. The basic functional equation for F is that F(t/b) = [
Journal ArticleDOI
Some results on uniformly high-order accurate essentially nonoscillatory schemes
TL;DR: This paper constructs an hierarchy of uniformly high-order accurate approximations of any desired order of accuracy which are tailored to be essentially nonoscillatory.
Journal ArticleDOI
Multiresolution representation of data: a general framework
TL;DR: A general framework for a multiresolution representation of data which is obtained by the discretization of mappings is presented, which allows for nonlinear (data-dependent) multiresolved representation schemes and thus enables us to design adaptive data-compression algorithms.