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.

Wavelet-Based Event Detection Method Using PMU Data

Abstract: In order to deal with the nonstationary signatures of phasor measurement units (PMU) signals, this paper presents a wavelet-based detection algorithm. Moreover, for an application to PMU for event detection purpose, it is necessary for us to classify detected events into unexpected real power related accidents, such as generator trip or automated control, such as reactive power injection. The proposed normalized wavelet energy function calculates the root mean square (RMS) of detail coefficients from time-synchronized voltage and frequency that reflect nonstationary occurrence of significant changes in signals. For a robust detection, wavelet-based detection parameter is designed with consideration of nonstationary characteristics of events. Also, there are distinct transients in voltage and frequency caused by different event types, and distinct results are key-idea of event classification. Besides the determination of event occurrences, one can obtain the information of event characteristics that include event types and zonal information of event from the proposed method. Moreover, successful results of detection and classification in real-world cases are presented in this paper.

Feature-based wavelet shrinkage algorithm for image denoising

Abstract: A selective wavelet shrinkage algorithm for digital image denoising is presented. The performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings. The improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods. The denoising method incorporated in the proposed algorithm involves a two-threshold validation process for real-time selection of wavelet coefficients. The two-threshold criteria selects wavelet coefficients based on their absolute value, spatial regularity, and regularity across multiresolution scales. The proposed algorithm takes image features into consideration in the selection process. Statistically, most images have regular features resulting in connected subband coefficients. Therefore, the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients. In the proposed algorithm, coefficients are selected due to their magnitude, and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction. Therefore, two thresholds are used in the coefficient selection process. The first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity. The performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques, as well as being computationally efficient to facilitate real-time image-processing applications.

Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I

Abstract: A generalization of Harten's multiresolution algorithms to two-dimensional (2-D) hyperbolic conservation laws is presented. Given a Cartesian grid and a discretized function on it, the method computes the local-scale components of the function by recursive diadic coarsening of the grid. Since the function's regularity can be described in terms of its scale or multiresolution analysis, the numerical solution of conservation laws becomes more efficient by eliminating flux computations wherever the solution is smooth. Instead, in those locations, the divergence of the solution is interpolated from the next coarser grid level. First, the basic 2-D essentially nonoscillatory (ENO) scheme is presented, then the 2-D multiresolution analysis is developed, and finally the subsequent scheme is tested numerically. The computational results confirm that the efficiency of the numerical scheme can be considerably improved in two dimensions as well.

Using the refinement equation for the construction of pre-wavelets

Abstract: A variety of methods have been proposed for the construction of wavelets. Among others, notable contributions have been made by Battle, Daubechies, Lemarie, Mallat, Meyer, and Stromberg. This effort has led to the attractive mathematical setting of multiresolution analysis as the most appropriate framework for wavelet construction. The full power of multiresolution analysis led Daubechies to the construction ofcompactly supported orthonormal wavelets with arbitrarily high smoothness. On the other hand, at first sight, it seems some of the other proposed methods are tied to special constructions using cardinal spline functions of Schoenberg. Specifically, we mention that Battle raises some doubt that his block spin method “can produce only the Lemarie Ondelettes”. A major point of this paper is to extend the idea of Battle to the generality of multiresolution analysis setup and address the easier job of constructingpre-wavelets from multiresolution.