Two-dimensional Haar Wavelet Research Articles

Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium

This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution.

An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders

In this paper, a novel technique is being formulated for the numerical solution of integral equations (IEs) as well as integro-differential equations (IDEs) of first and higher orders. The present approach is an improved form of the Haar wavelet methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). The proposed modifications resulted in computational efficiency and simple applicability of the earlier methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). In addition to this, the new approach is being extended from IDEs of first order to IDEs of higher orders with initial- and boundary-conditions. Unlike the methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013) (where the kernel function is being approximated by two-dimensional Haar wavelet), the kernel function in the present case is being approximated by one-dimensional Haar wavelet. The modified approach is easily extendable to higher order IDEs. Numerical examples are being included to show the accuracy and efficiency of the new method.

Two-dimensional wavelets for numerical solution of integral equations

Purpose: In this paper, we shall investigate the numerical solution of two-dimensional Fredholm integral equations (2D-FIEs). Methods: In this work, we apply two-dimensional Haar wavelets, to solve linear two dimensional Fredholm integral equations (2D-FIEs). Using 2D Haar wavelets and their properties, 2D-FIEs of the second kind reduce to a system of algebraic equations. Results: The numerical examples illustrate the efficiency and accuracy of the method. Conclusions: In comparison with other bases (for example, polynomial bases), one of the advantages of this method is, although the involved matrices have a large dimension, they contain a large percentage of zero entries, which keeps computational effort within reasonable limits.

A wavelet approach to the terrain correction in gravimetry and gravity gradiometry

A traditional, standard method to compute the gravitational effect of the topographic masses uses a finite element decomposition into right rectangular, vertical prisms, one for each terrain elevation data point. An alternative construction is proposed based on the two-dimensional Haar wavelet, which ultimately is identical, but instead slices the topography into horizontal slabs. It is shown that far fewer such slabs need to be accounted to obtain the same accuracy in the gravitational effect, or, also, the terrain correction. The method is tested on first and second derivatives of the gravitational potential in areas of relatively gentle and rough terrains.

FPGA-based IP cores implementation for face recognition using dynamic partial reconfiguration

This paper presents a combination of novel feature vectors construction approach for face recognition using discrete wavelet transform (DWT) and field programmable gate array (FPGA)-based intellectual property (IP) core implementation of transform block in face recognition systems. Initially, four experiments have been conducted including the DWT feature selection and filter choice, features optimisation by coefficient selections and feature threshold. To examine the most suitable method of feature extraction, different wavelet quadrant and scales have been evaluated, and it is followed with an evaluation of different wavelet filter choices and their impact on recognition accuracy. In this study, an approach for face recognition based on coefficient selection for DWT is presented, and the significant of DWT coefficient threshold selection is also analysed. For the hardware implementation, two architectures for two-dimensional (2-D) Haar wavelet transform (HWT) IP core with transpose-based computation and dynamic partial reconfiguration (DPR) have been synthesised using VHDL and implemented on Xilinx Virtex-5 FPGAs. Experimental results and comparisons between different configurations using partial and non-partial reconfiguration processes and a detailed performance analysis of the area, power consumption and maximum frequency are also discussed in this paper.

Solving PDEs with the aid of two-dimensional Haar wavelets

Two-dimensional Haar wavelets are applied for solution of the partial differential equations (PDEs). The proposed method is mathematically simple and fast. To demonstrate the efficiency of the method, two test problems (solution of the diffusion and Poisson equations) are discussed. Computer simulation showed that the method guarantees the necessary exactness already for a small number of grid points.

Effective processing of continuous group-by aggregate queries in sensor networks

Abstract Aggregate queries are one of the most important queries in sensor networks. Especially, group-by aggregate queries can be used in various sensor network applications such as tracking, monitoring, and event detection. However, most research has focused on aggregate queries without a group-by clause. In this paper, we propose a framework, called the G-Framework, to effectively process continuous group-by aggregate queries in the environment where sensors are grouped by the geographical location. In the G-Framework, we can perform energy effective data aggregate processing and dissemination using two-dimensional Haar wavelets. Also, to process continuous group-by aggregate queries with a HAVING clause, we divide data collection into two phases. We send only non-filtered data in the first collection phase, and send data requested by the leader node in the second collection phase. Experimental results show that the G-Framework can process continuous group-by aggregate queries effectively in terms of energy consumption.

Comparison of the efficiencies of image compression algorithms based on separable and nonseparable two-dimensional Haar wavelet bases

Compression algorithms for digital images are described that are based on nonseparable two-dimensional wavelet transforms on nonrectangular supports. The efficiencies of these algorithms are experimentally investigated and compared with those of a compression algorithm based on a separable Haar wavelet basis.

Nondestructive damage evaluation of plates using the multi-resolution analysis of two-dimensional Haar wavelet

A wavelet application to the vibration-based damage evaluation technique is introduced. The proposed method requires only a few of the lower mode shapes before and after a small damage event in order to detect, locate, and size damage on plate-like structures. The proposed method takes account for uncertainty in mass density, surrounding forces, foundation stiffness, etc. Based on a small damage assumption of a thin plate, the two-dimensional damage index (DI) equation is revealed within the context of elasticity. The singularity problem, which occurs in the resulting DI equation, is solved in the two-dimensional multi-resolution wavelet domain with the aid of the singular value decomposition technique. Finally, the desired damage measures are reconstructed from the one in the wavelet space by inverse wavelet transformation. The performance of the proposed method is compared with an existing damage detection method. Finally, an uncertainty analysis of the proposed method is provided.

Comparison of feature extraction and selection methods in mammogram recognition.

This paper presents a comparison of feature extraction and selection methods in the design of mammogram recognition systems. Mammographic images were classified into two categories, normal and cancerous. The following methods of feature extraction were investigated: two-dimensional Haar wavelets, histograms, and singular value decomposition. The feature patterns were reduced and selected using principal component analysis (PCA) and rough sets. The rough sets methods were applied to the final selection of the pattern features. Classification of mammograms was realized using an error backpropagation neural network.

On the implementation of nonseparable two-dimensional Haar wavelet transforms

We introduce a transformation to localize the equations defining the successive levels of the Mallat (1989) pyramid for two-dimensional (2-D) Haar wavelets. We propose a methodology for implementing these wavelet transforms in parallel architectures like systolic arrays. More specifically, we show that there is a perfect match between the wavelet algorithms and the multiphase multirate array (MPRA) architectures.