The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform, has been shown to be potentially useful for signal processing. Many fundamental results of this transform are already known, but the theory of multiresolution analysis and orthogonal wavelets is still missing. In this paper, we first develop multiresolution analysis associated with the FRWT and then deri...

AbstractIn this paper, we evaluate the performance of a spatial multiresolution analysis (SMA) method, that behaves like variable bandwidth kernel density estimation (KDE) for hazardous r...

Multiresolution motion analysis has gained considerable research interest as a unified framework to facilitate a variety of motion editing tasks. Within this framework, motion data are represented as a collection of coefficients that form a coarseto-fine hierarchy. The coefficients at the coarsest level describe the global pattern of a motion signal, while those at fine levels provide details a...

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...

Pansharpening technique is used to merge the original multispectral image (MS) with a high spatial resolution panchromatic (PAN). Due its robustness, multiresolution analysis (MRA) an important part of pansharpening. The scale regression model effective for improving MRA. However, existing MRA based on results into single-scale information, thus affecting final pansharpening result. To address ...

We propose a new subdivision scheme derived from the Lounsbery’s regular 1:4 face split, allowing multiresolution analysis of irregularly subdivided triangular meshes by the wavelet transforms. Some experimental results on real medical meshes prove the efficiency of this approach in multiresolution schemes. In addition we show the effectiveness of the proposed algorithm for lossless compression.

Efficiency of high-order essentially non-oscillatory (ENO) approximations of conservation laws can be drastically improved if ideas of multiresolution analysis are taken into account. These methods of data compression not only reduce the necessary amount of discrete data but can also serve as tools in detecting local low-dimensional features in the numerical solution. We describe the mathematic...

Multiresolution analysis is an established part of the human vision system. It builds different representations of an image with a spatial resolution adapted to the size of objects of interest and to its level of relevance. Multiresolution analysis is an efficient tool for image segmentation. It allows the processing of global features as well as local features in a corresponding proper scale. ...

In order to investigate turbulent phenomena in compressible flows the Variational Multiscale method is used. This method is usually applied to incompressible flows. In a first step, we derive the VMS method for the compressible Navier-Stokes equations. The resulting weak formulation of the flow equations is split into resolved and unresolved scales using multiresolution techniques based on bior...