Multi-wavelets from B-spline super-functions with approximation order

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.

Wavelets/multiwavelets bases and correspondence estimation problem : an analytic study

Correspondence estimation in one of the most active research areas in the field of computer vision and number of techniques has been proposed, possessing both advantages and shortcomings. Among the techniques reported, multiresolution analysis based stereo correspondence estimation has gained lot of research focus in recent years. Although, the most widely employed medium for multiresolution analysis is wavelets and multiwavelets bases, however, relatively little work has been reported in this context. In this work we have tried to address some of the issues regarding the work done in this domain and the inherited shortcomings. In the light of these shortcomings, we propose a new technique to overcome some of the flaws that could have significantly impact on the algorithm performance and has not been addressed in the earlier propositions. Proposed algorithm uses multiresolution analysis enforced with wavelets/multiwavelts transform modulus maxima to establish correspondences between the stereo pair of images. Variety of wavelets and multiwavelets bases, possessing distinct properties such as orthogonality, approximation order, short support and shape are employed to analyse their effect on the performance of correspondence estimation. The idea is to provide knowledge base to understand and establish relationships between wavelets and multiwavelets properties and their effect on the quality of stereo correspondence estimation.

Construction of wavelets and multiwavelets basis : a generalized method

Multiwavelets are wavelets with multiplicity r, that is r scaling functions and r wavelets, which define multiresolution analysis similar to scalar wavelets. They are advantageous over scalar wavelets since they simultaneously posse symmetry and orthogonality. In this work, a new method for constructing multiwavelets with any approximation order is presented. The method involves the derivation of a matrix equation for the desired approximation order. The condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors give the combinations of scaling functions required to reconstruct the desired spline or super function. The method is demonstrated by constructing a specific class of symmetric and non-symmetric multiwavelets with different approximation orders, which include Geranimo-Hardin-Massopust (GHM), Daubechies and Alperts like multi-wavelets, as parameterized solutions. All multi-wavelets constructed in this work, posses the good properties of orthogonality, approximation order and short support.

Stereo vision and wavelets/multiwavelets analysis : 3d reconstruction using wavelets/multiwavelets theory and stereo vision

During the image formation process of the camera, explicit 3D information about the scene or objects in the scene are lost. Therefore, 3D structure or depth information has to be inferred implicitly from the 2D intensity images. This problem is com- monly referred to as 3D reconstruction. In this work a complete 3D reconstruction algorithm is presented, capable of reconstructing dimensionally accurate 3D models of the objects, based on stereo vision and multi-resolution analysis. The developed system uses a reference depth model of the objects under observation to improve the disparity maps, estimated. Only a few features are extracted from that reference model, which are the relative location of the discontinuities and the z-dimensional extremes of objects depth. The maximum error deviation of the estimated depth along the surfaces is less than 0.5mm and along the discontinuities is less than 1.5mm. The developed system is invariant to illuminative variations, and orientation, location and scaling of the objects under consideration, which makes the developed system highly robust.

Text-dependent speaker recognition using wavelets and neural networks

An intelligent system for text-dependent speaker recognition is proposed in this paper. The system consists of a wavelet-based module as the feature extractor of speech signals and a neural-network-based module as the signal classifier. The Daubechies wavelet is employed to filter and compress the speech signals. The fuzzy ARTMAP (FAM) neural network is used to classify the processed signals. A series of experiments on text-dependent gender and speaker recognition are conducted to assess the effectiveness of the proposed system using a collection of vowel signals from 100 speakers. A variety of operating strategies for improving the FAM performance are examined and compared. The experimental results are analyzed and discussed.

Development of a speaker recognition system using wavelets and artificial neural networks

This paper addresses the problem of speaker recognition from speech signals. The study focuses on the development of a speaker recognition system comprising two modules: a wavelet-based feature extractor, and a neural-network-based classifier. We have conducted a number of experiments to investigate the applicability of Discrete Wavelet Transform (D WT) in extracting discriminative features from the speech signals, and have examined various models from the Adaptive Resonance Theory (ART) family of neural networks in classijjing the extracted features. The results indicate that DWT could be a potential feature extraction tool for speaker recognition. In addition, the ART-based classijiers have yielded very promising recognition accuracy at more than 81%.

Classification of healthcare data using genetic fuzzy logic system and wavelets

Healthcare plays an important role in promoting the general health and well-being of people around the world. The difficulty in healthcare data classification arises from the uncertainty and the high-dimensional nature of the medical data collected. This paper proposes an integration of fuzzy standard additive model (SAM) with genetic algorithm (GA), called GSAM, to deal with uncertainty and computational challenges. GSAM learning process comprises three continual steps: rule initialization by unsupervised learning using the adaptive vector quantization clustering, evolutionary rule optimization by GA and parameter tuning by the gradient descent supervised learning. Wavelet transformation is employed to extract discriminative features for high-dimensional datasets. GSAM becomes highly capable when deployed with small number of wavelet features as its computational burden is remarkably reduced. The proposed method is evaluated using two frequently-used medical datasets: the Wisconsin breast cancer and Cleveland heart disease from the UCI Repository for machine learning. Experiments are organized with a five-fold cross validation and performance of classification techniques are measured by a number of important metrics: accuracy, F-measure, mutual information and area under the receiver operating characteristic curve. Results demonstrate the superiority of the GSAM compared to other machine learning methods including probabilistic neural network, support vector machine, fuzzy ARTMAP, and adaptive neuro-fuzzy inference system. The proposed approach is thus helpful as a decision support system for medical practitioners in the healthcare practice.

Medical diagnosis by fuzzy standard additive model with wavelets

This paper proposes a combination of fuzzy standard additive model (SAM) with wavelet features for medical diagnosis. Wavelet transformation is used to reduce the dimension of high-dimensional datasets. This helps to improve the convergence speed of supervised learning process of the fuzzy SAM, which has a heavy computational burden in high-dimensional data. Fuzzy SAM becomes highly capable when deployed with wavelet features. This combination remarkably reduces its computational training burden. The performance of the proposed methodology is examined for two frequently used medical datasets: the lump breast cancer and heart disease. Experiments are deployed with a five-fold cross validation. Results demonstrate the superiority of the proposed method compared to other machine learning methods including probabilistic neural network, support vector machine, fuzzy ARTMAP, and adaptive neuro-fuzzy inference system. Faster convergence but higher accuracy shows a win-win solution of the proposed approach.