Multiresolution Analysis Theory Research Articles

A Feasible Algorithm for Designing Biorthogonal Binary Finitely Supported Multiwavelet Functions

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, the notion of vector-valued multiresolution analysis is introduced and the definition of the biorthogonal vector-valued bivariate wavelet functions is given. The existence of biorthogonal vector-valued binary wavelet functions associated with a pair of biorthogonal vector-valued finitely supported binary scaling functions is investigated. An algorithm for constructing a class of biorthogonal vector-valued finitely supported binary wavelet functions is presented by virtue of multiresolution analysis and matrix theory.

Based on the Minimum Variance Spectral Estimation of Radar Wind Profile Analysis

In this paper, we apply minimum variance method for removing automatically ground and intermittent clutter (airplane echo) from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop Doppler echo power spectral, which allow us to identify the coefficients relevant for clutter and to suppress them in order to effectively restrain and remove clutter and increase the wind profile radar detection range and accuracy; must be on the air back to the effective spectrum of the spectral moments estimation. Using MATLAB simulation analysis , compared with the conventional method of analysis to verify the feasibility and effectiveness of the algorithm, also, try the algorithm is applied to the complexity of the weather with a strong interference case of precipitation particles; Data analysis showed that the actual detection, from the library in the lower spectrum moment estimation has been improved significantly.

Constructional Approaches on Vector-Valued Wavelets with Multi-Scale Dilation Factor

In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for construc- -ting a class of biorthogonal finitely supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory. A sufficient condition for the existence of multiple pseudoframes for subspaces is derived

Harris Corner Detection Algorithm Based on Improved Contourlet Transform

According to multi-resolution analysis theory, this paper constructed a new Harris multi-scale corner detection algorithm based on contourlet transform. The algorithm can be decomposed by contourlet under different scales, and extract feature points on the edge direction, obtain the corner. The new algorithm can also overcome phenomenon caused by the single-scale Harris corner detection such as the loss information of corners, the corner position offset and extract false corners disturbed by noise. Experimental results show that the new corner algorithm detected more uniform distribution and reasonable, can be well applied in many fields such as image stitching.

New fuzzy wavelet network for modeling and control: The modeling approach

In this paper, a fuzzy wavelet network is proposed to approximate arbitrary nonlinear functions based on the theory of multiresolution analysis (MRA) of wavelet transform and fuzzy concepts. The presented network combines TSK fuzzy models with wavelet transform and ROLS learning algorithm while still preserve the property of linearity in parameters. In order to reduce the number of fuzzy rules, fuzzy clustering is invoked. In the clustering algorithm, those wavelets that are closer to each other in the sense of the Euclidean norm are placed in a group and are used in the consequent part of a fuzzy rule. Antecedent parts of the rules are Gaussian membership functions. Determination of the deviation parameter is performed with the help of gold partition method. Here, mean of each function is derived by averaging center of all wavelets that are related to that particular rule. The overall developed fuzzy wavelet network is called fuzzy wave-net and simulation results show superior performance over previous networks. The present work is complemented by a second part which focuses on the control aspects and to be published in this journal( [17]). This paper proposes an observer based self-structuring robust adaptive fuzzy wave-net (FWN) controller for a class of nonlinear uncertain multi-input multi-output systems.

Constructive Algorithm to Two-Directional Biorthogonal Shortly Supported Wavelets with Poly-Scale Dilation Factor

In this work, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelet packets is proposed and their properties is investigated by means of time-frequency analysis methodand, operator theory. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for designing a class of biorthogonal shortly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

Existence and Designment of Filter Banks of Biorthogonal Vector-Valued Wavelets with Three-Scale Constant Factor

In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for constructing a class of biorthogonal compactly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

2-Adic wavelet bases

Within the theory of multiresolution analysis, a method of constructing 2-adic wavelet systems that form Riesz bases in L2(ℚ2) is developed. A realization of this method for some infinite family of multiresolution analyses leading to nonorthogonal Riesz bases is presented.

Semiorthogonal Multiresolution Analysis Frames in Higher Dimensions

Benedetto and Li proposed the theory of frame multiresolution analysis (FMRA) in one dimension. This paper generalizes Benedetto and Li’s theory of FMRA to higher dimensions with arbitrary integral expansive matrix dilations, and gives two necessary and sufficient conditions to characterize (semiorthogonal) multiresolution analysis frames for L2(ℝn). One of the two conditions is put on the frame scaling function and the low-pass and high-pass filters only. Multiresolution analysis Parseval frames are also characterized. The theory is implemented to a bidimensional example with the nonseparable quincunx dilation \(\scriptsize\bigl(\begin{array}{c@{\ }c}1&-1\\1&1\end{array}\bigr)\) , along with its potential application in subband signal processing.

Construction and decomposition of biorthogonal vector-valued wavelets with compact support

In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.

Radar target recognition based on the multi-resolution analysis theory and neural network

One-dimension range profile has recently been widely used as recognition feature in radar target recognition since it can be extracted easily. However, the one-dimension range profile of a target has strong dependence on the aspect-angle of the target because it is based on the model of scattering centers. On the other hand, the different classes of target samples overlap each other in the feature space, so satisfactory recognition results cannot be obtained directly for the targets under whole posture. In order to improve the recognition performance of systems based on one-dimension range profile, a method of radar target recognition based on the multi-resolution analysis theory and neural network is presented. Firstly, one-dimension range profile features under various resolutions are obtained by using multi-resolution analysis. Then, the tree-structured cascade SOM network – a hybrid neural network on the basis of the multi-resolution analysis theory and self-organizing map (SOM) – has been used as the classifier to make multi-grade judgment and recognition gradually for the one-dimension range profile features. The experimental results show that the average correct recognition rate for three kinds of targets – a propeller aircraft, a little jet aircraft and a large jet aircraft – with 0–180° posture variation in aspect-angle is up to 92.97%.

Design and properties of vector-valued wavelets associated with an orthogonal vector-valued scaling function

The notion of vector-valued wavelets associated with an orthogonal vector-valued scaling function with 3-scale is introduced. The existence of orthogonal vector-valued wavelets is discussed and a necessary and sufficient condition is presented by means of the theory of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a class of orthogonal vector-valued wavelets with compact support is proposed. The concept of vector-valued wavelet packets is introduced and their properties are characterized by virtue of operator theory, time–frequency analysis method. Moreover, it is shown how to construct various orthonormal bases of space L 2 ( R , C μ ) ( 2 ⩽ μ ∈ Z ) from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

The research of a class of biorthogonal compactly supported vector-valued wavelets

In this paper, we introduce the biorthogonal vector-valued wavelets. We prove that, like in the scalar wavelet case, the existence of a pair of biorthogonal compactly supported vector-valued scaling functions guarantees the existence of a pair of biorthogonal compactly supported vector-valued wavelet functions. An algorithm for constructing a pair of biorthogonal compactly supported vector-valued wavelet functions is presented by means of vector-valued multiresolution analysis and matrix theory. The notion of biorthogonal vector-valued wavelet packets is introduced, and their properties are investigated by virtue of time–frequency analysis and algebra theory. Three biorthogonality formulas concerning the wavelet packets are established. Relation to some physical theories such as E-infinity Cantorian space–time theory is also discussed.

Assessing the multi-resolution information content of remotely sensed variables and elevation for evapotranspiration in a tall-grass prairie environment

Understanding the spatial scaling behavior of evapotranspiration and its relation to controlling factors on the land surface is necessary to accurately estimate regional water cycling. We propose a method for ascertaining this scaling behavior via a combination of wavelet multi-resolution analysis and information theory metrics. Using a physically-based modeling framework, we are able to compute spatially distributed latent heat fluxes over the tall-grass prairie in North-central Kansas for August 8, 2005. Comparison with three eddy-covariance stations and a large aperture scintillometer demonstrates good agreement, and thus give confidence in the modeled fluxes. Results indicate that the spatial variability in radiometric temperature (a proxy for soil moisture) most closely controls the spatial variability in evapotranspiration. Small scale variability in the water flux can be ascribed to the small scale spatial variance in the fractional vegetation. In addition, correlation analysis indicates general scale invariance and that low spatial resolution data may be adequate for accurately determining water cycling in prairie ecosystems.

Adaptive fuzzy wavelet network control design for nonlinear systems

This paper presents a new adaptive fuzzy wavelet network controller (A-FWNC) for control of nonlinear affine systems, inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts. The proposed adaptive gain controller, which results from the direct adaptive approach, has the ability to tune the adaptation parameter in the THEN-part of each fuzzy rule during real-time operation. Each fuzzy rule corresponds to a sub-wavelet neural network (sub-WNN) and one adaptation parameter. Each sub-WNN consists of wavelets with a specified dilation value. The degree of contribution of each sub-WNN can be controlled flexibly. Orthogonal least square (OLS) method is used to determine the number of fuzzy rules and to purify the wavelets for each sub-WNN. Since the efficient procedure of selecting wavelets used in the OLS method is not very sensitive to the input dimension, the dimension of the approximated function does not cause the bottleneck for constructing FWN. FWN is constructed based on the training data set of the nominal system and the constructed fuzzy rules can be adjusted by learning the translation parameters of the selected wavelets and also determining the shape of membership functions. Then, the constructed adaptive FWN controller is employed, such that the feedback linearization control input can be best approximated and the closed-loop stability is guaranteed. The performance of the proposed A-FWNC is illustrated by applying a second-order nonlinear inverted pendulum system and compared with previously published methods. Simulation results indicate the remarkable capabilities of the proposed control algorithm. It is worth noting that the proposed controller significantly improves the transient response characteristics and the number of fuzzy rules and on-line adjustable parameters are reduced.

Four-bank compactly supported bisymmetric orthonormal wavelets bases

We define a new concept of bisymmetry for multibank wavelets. By extending the theory of multiresolution analysis to multibank wavelets, this work also focuses on the study of four-bank compactly supported bisymmetric orthonormal wavelets. Investigations have shown that there is a class of four-bank compactly supported orthonormal wavelets with bisymmetry, in which any wavelet system can be determined uniquely by its low-pass filter. Thus, the least restrictive conditions are needed for forming a wavelet, so that the free degrees can be reserved for application requirements. Also, such wavelet classes can be parameterized. Therefore, the optimal four-bank wavelets with bisymmetry can be found in this class. Some concrete examples with high vanishing moments are also given. These wavelets can avoid prefiltering, process the boundary conveniently, and enjoy the highly efficient computations in application.

Effect of time-dependent basis functions and their superposition error on atom-centered density matrix propagation (ADMP): connections to wavelet theory of multiresolution analysis.

We present a rigorous analysis of the primitive Gaussian basis sets used in the electronic structure theory. This leads to fundamental connections between Gaussian basis functions and the wavelet theory of multiresolution analysis. We also obtain a general description of basis set superposition error which holds for all localized, orthogonal or nonorthogonal, basis functions. The standard counterpoise correction of quantum chemistry is seen to arise as a special case of this treatment. Computational study of the weakly bound water dimer illustrates that basis set superposition error is much less for basis functions beyond the 6-31+G(*) level of Gaussians when structure, energetics, frequencies, and radial distribution functions are to be calculated. This result will be invaluable in the use of atom-centered Gaussian functions for ab initio molecular dynamics studies using Born-Oppenheimer and atom-centered density matrix propagation.

Adaptive multiresolution and wavelet-based search methods

New adaptive search methods based on multiresolution analysis and wavelet theory are introduced and discussed within the framework of the Markov theory. These stochastic search methods are suited to problems for which good solutions tend to cluster within the search space. Multiresolution search methods are extended to searches with memory. The introduction of a memory allows an easy inclusion of local information available before the search and the storage of a low-resolution approximation of the fitness function. In addition, by using B-splines, a linguistic, fuzzy interpretation of the search results can be given. The relation between wavelet-based search methods and wavelet estimation theory is explained. © 2004 Wiley Periodicals, Inc.

Wavelet based methods for improved wind profiler signal processing

Abstract. In this paper, we apply wavelet thresholding for removing automatically ground and intermittent clutter (airplane echoes) from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop wavelet domain thresholding rules, which allow us to identify the coefficients relevant for clutter and to suppress them in order to obtain filtered reconstructions.Key words. Meteorology and atmospheric dynamics (instruments and techniques) – Radio science (remote sensing; signal processing)

Fuzzy wavelet networks for function learning

Inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts, a fuzzy wavelet network (FWN) is proposed for approximating arbitrary nonlinear functions. The FWN consists of a set of fuzzy rules. Each rule corresponding to a sub-wavelet neural network (WNN) consists of single-scaling wavelets. Through efficient bases selection, the dimension of the approximated function does not cause the bottleneck for constructing FWN. Especially, by learning the translation parameters of the wavelets and adjusting the shape of membership functions, the model accuracy and the generalization capability of the FWN can be remarkably improved. Furthermore, an algorithm for constructing and training the fuzzy wavelet networks is proposed. Simulation examples are also given to illustrate the effectiveness of the method.