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.

Multi-resolution dyadic wavelet denoising approach for extraction of visual evoked potentials in the brain

Abstract: More powerful techniques need to be developed to extract small and weak visual evoked potentials (VEPs) from the spontaneous cerebral electric activity EEG. The authors present a wavelet decomposition algorithm suitable for identification and detection of very weak VEPs. The cross-correlation analysis between Daubechies wavelet (i.e. dbN) functions /spl psi//sub N/(t), for N=4, 5 ,...,10 and a representative noiseless VEP signal is performed to choose the proper wavelet function, say that with maximum correlation coefficient (highest resemblance) with respect to the representative VEP signal sequence. In this way, the specific choice of the best wavelet prototype function is no longer arbitrary for the application of obtaining pattern reversal VEPs. Extensive clinical experiments have demonstrated that the multiresolution wavelet analysis method can identify and estimate the peak latency of VEP signal well, with only a much reduced trial of ensemble averaging (EA) required. The major advantages of the wavelet transform are that it can 'zoom-in' to time discontinuities, and that orthonormal bases, localised in time and frequency, can be constructed. With this zoom-in property of the wavelet analysis, the irregularities or abnormalities of signals can easily be detected. Also the characteristics of EP signals can be captured by means of wavelet analysis, which can be further used for the detection and recognition of the abnormalities in the brain.

High-order Runge-Kutta multiresolution time-domain methods for computational electromagnetics

Abstract: In this paper we introduce a class of Runge-Kutta multiresolution time-domain (RK-MRTD) methods for problems of electromagnetic wave propagation that can attain an arbitrarily high order of convergence in both space and time. The methods capitalize on the high-order nature of spatial multiresolution approximations by incorporating time integrators with convergence properties that are commensurate with these. More precisely, the classical MRTD approach is adapted here to incorporate mth-order m-stage low-storage Runge-Kutta methods for the time integration. As we show, if compactly supported wavelets of order N are used (e.g., the Daubechies DN functions) and m=N, then the RK-MRTD methods deliver solutions that converge with this overall order; a variety of examples illustrate these properties. Moreover, we further show that the resulting algorithms are well suited to parallel implementations, as we present results that demonstrate their near-optimal scaling

Interpretation of ground penetrating radar image using digital wavelet transform

Abstract: The ultra wide bandwidth nature of ground penetrating radar antenna has made a raw data acquired with the tool prone to unwanted noise and hence low signal to noise ratio. Quantitative interpretation of the data is desirable for radar image quality enhancement. This study used multiresolution analysis to process radar image at different levels of decomposition. Daubechie wavelets family was used to decompose the image into 4-different levels of details. Level 3 diagonal details and level 4 horizontal details provide a noise-free visualization of the subsurface discontinuities. This led to the detection of buried utility and unique identification of its spatial location. The depth of the buried utility was estimated based on the image scale. The work demonstrates the effectiveness of Daubechie wavelet transform analysis as yet another technique of utility survey data acquired with GPR.

Content-Based Image Retrieval Via the Multiresolution Wavelet Features of Interest

Abstract: For the purpose of efficiently and effectively retrieving the desired images from a large image database, the development of a user-friendly image retrieval system is indispensable. In this paper, we propose a contentbased image retrieval method based on the discrete wavelet transform (DWT) that is possessed of the superiority in multiresolution analysis and spatial-frequency localization. Further, to bridge the gap between the retrieving results and the users' expectation, we developed an interactive user interface such that the users can adjust the weights for each wavelet feature according to their expectations. Then, the system will retrieve the images that are most satisfied to the users' need from the image database via the selected multiresolution wavelet features of interest. We have performed experiments on a database with 1000 images and the results show the effectiveness of our approach.

Adaptive multiresolution analysis based on anisotropic triangulations

Abstract: A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function ƒ of two variables, the algorithm produces a hierarchy of triangulations (Dj )j≥0 and piecewise polynomial approximations of ƒ on these triangulations. The refinement procedure consists in bisecting a triangle Τ in a direction which is chosen so as to minimize the local approximation error in some prescribed norm between ƒ and its piecewise polynomial approximation after Τ is bisected. The hierarchical structure allows us to derive various approximation tools such as multiresolution analysis, wavelet bases, adaptive triangulations based either on greedy or optimal CART trees, as well as a simple encoding of the corresponding triangulations. We give a general proof of convergence in the Lp norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of ƒ in case of C2 functions).