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.

Analysis of dynamic stress concentration problems employing spline-based wavelet Galerkin method

Abstract: Two-dimensional (2D) dynamic stress concentration problems are analyzed using the wavelet Galerkin method (WGM). Linear B-spline scaling/wavelet functions are employed. We introduce enrichment functions for the X-FEM to represent a crack geometry. In the WGM, low-resolution scaling functions are periodically located across the entire analysis domain to approximate deformations of a body. High-resolution wavelet functions and enrichment functions including crack tip singular fields are superposed on the scaling functions to represent the severe stress concentration around holes or crack tips. Heaviside functions are also enriched to treat the displacement discontinuity of the crack face. Multiresolution analysis of the wavelet basis functions plays an important role in the WGM. To simulate the transients, the wavelet Galerkin formulation is discretized using a Newmark-β time integration scheme. A path independent J-integral is adopted to evaluate the dynamic stress intensity factor (DSIF). We solve dynamic stress concentration problems and evaluate DSIF of 2D cracked solids. The accuracy and effectiveness of the proposed method are discussed through the numerical examples.

Predictive subband image coding with wavelet transform

Abstract: Wavelet transform can decompose images into various multiresolution subbands. In these subbands the correlation exists. A novel technique for image coding by taking advantage of the correlation is addressed. It is based on predictive edge detection from the LL band of the lowest resolution level to predict the edge in the LH, HL and HH bands in the higher resolution level. If the coefficient is predicted as an edge it is preserved; otherwise, it is discarded. In the decoder, the location of the preserved coefficients can also be found as in the encoder. Therefore, no overhead is needed. Instead of complex vector quantization, which is commonly used in subband image coding for high compression ratio, simple scalar quantization is used to code the remaining coefficients and achieves very good results.

A wavelet transform image coding technique with a quadtree structure

Abstract: Much work in image coding has centered on wavelet transforms, which can be used to generate multiresolution representation of images. Wavelet transforms have been shown to achieve high compression ratios while maintaining very good image quality, because edge characteristics of images can be well preserved by this method at low bit rates. Quadtree decomposition techniques also utilize the multiresolution nature of images of a segmentation device before coding. The implementation of a novel hybrid technique for coding the coefficients of a wavelet transformation which makes use of a quadtree structure is discussed. This method is a scalar coding technique which takes advantage of the correlation between different scales in the wavelet decomposition, while requiring much less computational complexity than a comparable full search vector quantization technique described. >

Application of wavelet analysis to upscaling of rock properties

Abstract: Although numerous upscaling techniques are reported in the literature, efficiently computing reasonably accurate equivalent rock properties from geological data at fine scale remains difficult. This is especially true for facies with multiple lithologies under multiphase flow conditions. Due to the nature of multiscale heterogeneity inherent in petroleum reservoirs, the equivalent rock and flow properties will vary with the scales of heterogeneity. Therefore, upscaled properties under multiphase flow conditions cannot be estimated without reference to the absolute scales of heterogeneity. Wavelet analysis is a multiresolution framework and, thus, it is well suited for upscaling rock and flow properties in a multiscale heterogeneous reservoir. The compact support property of the wavelet transform assures efficient computation. Choice of regularity provides a flexible way to control the smoothness of the resulting upscaling properties. In this study, a new procedure was developed to significantly improve the computational efficiency and accuracy of upscaling for generating equivalent rock and rock-fluid properties under various geological and flow conditions based on multiresolution analysis of wavelet transforms. Additionally, a wavelet reconstruction method was explored to provide a basis for downsampling fine-scale rock property fields from information at various levels of coarser scale. The beauty of the method is that sincemore » the equivalent properties at different length scales are computed recursively, the interdependent influences of the heterogeneities on the scales are included effectively. The method is demonstrated by successfully applying it to upscale interbedset and interfacies outcrop petrophysical data.« less