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 energy function for symmetrical fault detection during power swing

Abstract: Fault during power swing is one of the challenging task for the distance relay functioning. This paper focuses on developing Wavelet Energy (WE) based function for symmetrical fault detection during power swing. The process starts at retrieving the current signal samples during power swing and processes it through Wavelet Transform to derive detailed coefficient of wavelet d1 to d7, used to find out energy of the signal, and called Wavelet Energy (WE). In the case study, the three-phase symmetrical fault is created in the transmission line and proposed algorithm detects the fault with in one and half cycles for 60 Hz system. Simulation results demonstrate the effectiveness of the proposed approach under time-varying conditions.

An orthonormal–shell–fourier descriptor for rapid matching of patterns in image database

Abstract: Invariance and low dimension of features are of crucial significance in pattern recognition. This paper proposes a novel orthonormal shell Fourier descriptor that satisfies all of these demands. This method first performs orthonormal shell decomposition on the line moment that is obtained from the 2-D pattern, then applies Fourier transform on each scale of the shell coefficients. Unlike other existing wavelet-based methods, our method allows applying common orthonormal wavelets, such as Daubechies, Symmlet and Coiflet, therefore it is simple to implement. We study the structure of the filter used and develop a fast algorithm to rapidly compute the spectra of orthonormal shell coefficients. The complexity of the proposed descriptor is O(n log n). We apply a coarse-to-fine strategy to search the image database; the matching is very quick because of the multiscale feature structure. The effectiveness of this new descriptor is demonstrated by a series of experiments as well as the comparison with other descriptors. The proposed descriptor is robust to white noise.

Reducing subspace frame multiresolution analysis and frame wavelets

Abstract: Multiresolution analysis (MRA) and frame multiresolution analysis (FMRA) in $L^2(\mathbb R)$ play a significant role in the construction of wavelets and frame wavelets for $L^2(\mathbb R)$. In this paper, the notions of MRA and FMRA in a reducing subspace of $L^2(\mathbb R)$ are introduced, from which the construction of wavelets and frame wavelets for this subspace is obtained. Many examples are also provided to illustrate the general theory. In particular, most of them are about the space with its frequency lying in $[0,\infty)$, which is closely related to various Paley-Wiener Theorems.

Learning wavelet networks based on Multiresolution analysis: Application to images copy detection

Abstract: This paper proposes a new method for images contentbased copy detection through a wavelets network based on multiresolution. The system is not only able to detect image copies, but it is also able to detect similar images to the original reference. The idea of this method is to project both the original images and the test one on a MRWN (MultiResolution Wavelets Network). In fact, this kind of wavelets network is a hybrid one constituted by a combination of a neural network and a wavelet network. This later is used to measure intelligently the similarity through two filters: approximation filter and details filter. As the matter of fact, the use of wavelet networks has allowed us to create an efficient and robust system for image copy detection.