Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Efficient design of a low redundant Discrete Shearlet Transform

Abstract: Recently, there has been a huge interest in multiresolution representations that also perform a multidirectional analysis. The Shearlet transform provides both a multiresolution analysis (such as the wavelet transform), and at the same time an optimally sparse image-independent representation for images containing edges. Existing discrete implementations of the Shearlet transform havemainly focused on specific applications, such as edge detection or denoising, and were not designed with a low redundancy in mind (the redundancy factor is typically larger than the number of orientation subbands in the finest scale). In this paper, we present a novel design of a Discrete Shearlet Transform, that can have a redundancy factor of 2.6, independent of the number of orientation subbands, and that has many interesting properties, such as shift-invariance and self-invertability. This transform can be used in a wide range of applications. Experiments are provided to show the improved characteristics of the transform.

Multiselective pyramidal decomposition of images: Wavelets with adaptive angular selectivity

Abstract: Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention, for instance, works on directional wavelets, steerable filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets, etc. In general, features that are best represented are straight lines or smooth curves as those de. ning contours of objects ( e. g. in curvelets processing) or oriented textures ( e. g. wave atoms, ridgelet packets). However, real images present also a set of details less oriented and more isotropic, like corners, spots, texture components, etc. This paper develops an adaptive representation for all these image elements, ranging from highly directional ones to fully isotropic ones. This new tool can indeed be tuned relatively to these image features by decomposing them into a Littlewood-Paley frame of directional wavelets with variable angular selectivity. Within such a decomposition, 2D wavelets inherit some particularities of the biorthogonal circular multiresolution framework in their angular behavior. Our method can therefore be seen as an angular multiselectivity analysis of images. Two applications of the proposed method are given at the end of the paper, namely, in the fields of image denoising and N-term nonlinear approximation.

New principle based on wavelet transform for power system short-term load forecasting

Abstract: Analysing the frequency characteristics of the power load , a new method for the short-term load forecasting is presented based on the wavelet transform (WT), particularly the multiresolution analysis technique. By the WT, the different load sequence components are projected to the different scales in which the matching forecast methods can be used. The forecasting results are then obtained by the reconstruction of the forecast results in different scales. Simulation results demonstrate that the proposed method can offer higher forecast precision.