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.

Diagrammatic multiresolution analysis for electron correlations

Abstract: We present a multiscale treatment of electron correlations based on hyperbolic wavelet expansions of Jastrow-type correlation functions. Wavelets provide hierarchical basis sets that can be locally adapted to the length- and energy-scales of physical phenomena. Combined with hyperbolic tensor products and local adaptive refinement near the interelectron cusp, these wavelet bases enable sparse representations of Jastrow factors. The computational efficiency of wavelets in electronic structure calculations is demonstrated within the coupled electron-pair approximation (local ansatz). Based on a diagrammatic multiresolution analysis, we discuss various kinds of sparsity features for matrix elements required by the local ansatz. Sparsity originates from the hierarchical structure and vanishing moments property of wavelet bases. This led us to a recurrence scheme for the evaluation of matrix elements with almost linear computational complexity with respect to the size of the underlying isotropic 3d-wavelet basis. Numerical studies for selected diagrams are presented for a homogeneous electron gas.

A fast method for textural analysis of DCT-based image

Abstract: The multiresolution wavelet transform is an effective procedure in texture analysis. However, many images are still compressed by the methods based on the discrete cosine transform (DCT). Thus, decompression of the inverse DCT is required to yield the textural features based on the wavelet transform for the DCT-coded image. This investigation adopts the multiresolution reordered features in texture analysis. The proposed features are directly generated using the DCT coefficients of the encoded image. Comparisons between the subband-energy features extracted from the wavelet transform and the conventional DCT, using the Brodatz texture database, demonstrate that the proposed method offers the best textural pattern retrieval accuracy and yields a much higher classification rate. The proposed DCT features are expected to be very useful and efficient in retrieving and classifying texture patterns in large DCT-coded image databases.

A Multiresolution Analysis of Stock Market Volatility Using Wavelet Methodology DRAFT OF LICENTIATE THESIS "SHORT" VERSION! ∗

Abstract: The non-stationary character of stock market returns manifests itself through the volatility clustering effect and large jumps. An efficient way of representing a time series with such complex dynamics is given by wavelet methodology. With the help of a wavelet basis, the discrete wavelet transform (DWT) is able to break a time series with respect to a time-scale while preserving the time dimension and energy. Time-scale specific information is important if one accepts the view that stock market consists of heterogenous investors operating at different time-scales. Considerable more insight into the volatility dynamics is gained by looking at the data at several different time-scales. At small timescales, in particular, the locality of wavelet analysis allows one to fully exploit high-frequency data. In addition, the DWT is even faster than the fast Fourier transform, so it is ideally suited for analyzing large data sets. The ”large-scale aim” of this paper is to first introduce wavelet methodology and then to analyze high-frequency stock market volatility with it. In more detail, the data consists of 5-minute observations of Nokia Oyj at the Helsinki Stock Exchange

Combining wavelet invariant moments and relevance vector machine for SAR target recognition

Abstract: A new method to classify targets in SAR images is proposed in this paper. The method combines both the advantages of wavelet invariant moments and relevance vector machine (RVM). The wavelet invariant moments have the wavelet inherent property of multi-resolution analysis and moment invariants quality. We firstly extract wavelet invariant moments to indicate targets in SAR images, and then select the feature set with principal component analysis (PCA). Finally, the selected feature set is fed to RVM for training and classifying. The RVM can powerfully manage complex classification and regression problems basing on the concept of probabilistic Bayesian learning framework. We perform 2- class and 3-class classification experiments respectively. Test results show that wavelet invariant moments indicate the target effectively, and RVM performs better than K-nearest neighbourhood (K-NN), back propagation neural network (BPNN) and least square support vector machine (LSSVM).

IFS fractals and the wavelet transform

Abstract: Iterated function systems (IFSs) are capable of effectively describing complex shapes and textures by fractals. The interscale properties of such fractals are analyzed with the aid of the wavelet transform and general multiresolution analysis. The result is a formulation for homogeneous IFSs in general scale space which leads to a direct solution of the inverse problem of finding the IFS which best represents a given function. Multiscale techniques that are used in the analysis are discussed. Some previous results from the IFS literature are introduced. >