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.

Stabile biortogonale Spline-Waveletbasen auf dem Intervall

Abstract: Based on the family of biorthogonal pairs of scaling functions consisting of cardinal B-splines and compactly supported dual generators on the whole real line, as presented by Cohen, Daubechies and Feauveau, we are concerned with the cnstruction of a new biorthogonal multiresolution analysis on the interval, such that the corresponding wavelet bases realize any desired order of moment condition on the interval. In contrast to previous approaches we choose the well-established Schoenberg spline basis on the interval with equidistant knots for primal multiresolution which has already been used by Chui and Quak to construct semiorthogonal spline bases on the interval. After giving an overview of the concrete construction, we discuss the cavorable properties of the constructed basis functions. The subsequent construction of the associated wavelets relies on the known method of stable completions, which has been presented by Dahmen, Kunoth and Urban as a helpful tool in constructing wavelet bases on the interval. Due to the fact, that we use all inner scaling functions, we use a high number of inner wavelets, so that the number of constructed boundary wavelets is very low, compared to former approaches. This is also true for the related wavelet basis with homogeneous or complementary boundary conditions. In view of applications, there are two interesting questions. Firstly, we investigate the condition number of the corresponding wavelet transforms. Secondly, we treat the stiffness matrix of the Laplace operator concerning to our basis and show, that its condition number is much better than the condition number in other approaches.

An FDTD multigrid based on multiresolution analysis

Abstract: A number of publications have demonstrated that the application of the method of moments directly to Maxwell's equations allows for the use of multiresolution analysis in the time domain. The principles of multiresolution analysis are applied to derive a novel multigrid scheme for the finite difference time domain (FDTD) technique. For the first time in literature, a mathematical correct approach for this problem is presented which allows for a priori estimation of the error. A dispersion analysis illustrates the benefits of additional wavelets in the FDTD analysis.

A Novel Neuro-Wavelet Based Self-Tuned Wavelet Controller for IPM Motor Drives

Abstract: This paper presents a hybrid neuro-wavelet scheme for on-line tuning of a wavelet-based multiresolution PID (MRPID) controller in real-time for precise speed control of an interior permanent magnet synchronous motor (IPMSM) drive system under system uncertainties. In the wavelet-based MRPID controller, the discrete wavelet transform (DWT) is used to decompose the error between actual and command speeds into different frequency components at various scales. The MRPID controller parameters are tuned by the wavelet neural network (WNN) to ensure optimum performance of the drive system. The proposed neuro-wavelet based MRPID controller is trained online with adaptive learning rates in the closed-loop vector control of the IPMSM drive system. The adaptive learning rates are derived using discrete Lyapunov stability theorem so that the convergence of the tracking error is guaranteed in the closed-loop system. The performances of the proposed hybrid controller are investigated in both simulation and experiments at different dynamic operating conditions. The complete vector control scheme incorporating the proposed self-tuning MRPID controller is successfully implemented in real-time using the ds1102 digital signal processor board for the laboratory 1-hp IPM motor. The superior performances of the proposed WNN-based self-tuning MRPID controller are also validated over fixed-gain controllers.

Robust nonlinear wavelet transform based on median-interpolation

Abstract: It is well known that wavelet transforms can be derived from stationary linear refinement subdivision schemes. We discuss a special nonlinear refinement subdivision scheme-median-interpolation. It is a nonlinear cousin of Deslauriers-Dubuc (1992) interpolation and of average-interpolation. The refinement scheme is based on constructing polynomials which interpolate median functionals of the underlying object. The refinement scheme can be deployed in a multiresolution fashion to construct nonlinear pyramid schemes and associated forward and inverse transforms. We discuss the basic properties of this transform and its possible use in wavelet de-noising schemes for badly non-Gaussian data. Analytic and computational results are presented to show that the nonlinear pyramid has a very different performance compared to traditional wavelets when coping with non-Gaussian data.