The wavelet representation using orthonormal wavelet bases has received widespread attention. Recently M-band orthonormal wavelet bases have been constructed and compactly supported M-band wavelets have been parameterized 15, 12, 32, 17]. This paper gives the theory and algorithms for obtaining the optimal wavelet multiresolution analysis for the representation of a given signal at a predetermi...

We present a general framework for the design of a mother wavelet best adapted to a specific signal or to a class of signals. The filter’s coefficients are obtained via optimization of a smooth objective function. We develop an unconstrained gradient-based optimization algorithm for a discrete wavelet transform. The algorithm is extended to the joint optimization of the mother wavelet and of th...

This paper proposes a new structure of wavelet extreme learning machine i.e. an adaptive wavelet extreme learning machine (AW-ELM) for finger motion recognition using only two EMG channels. The adaptation mechanism is performed by adjusting the wavelet shape based on the input information. The performance of the proposed method is compared to ELM using wavelet (W-ELM0 and sigmoid (Sig-ELM) acti...

Under the general regression setup, yi = gi + ǫi, we are interested in estimating a possibly multivariate regression function g. The wavelet thresholding is a simple operation in the wavelet domain that selects the subset of wavelet coefficients corresponding to an estimator of g when back-transformed. We propose the selection of this subset in a semi-supervised fashion, in which a neighbor str...

In this paper we study a generalization of the Donoho-Johnstone denoising model for the case of the translation invariant wavelet transform. Instead of soft-thresholding coeecients of the classical orthogonal discrete wavelet transform, we study soft-thresholding of the co-eecients of the translation invariant discrete wavelet transform. This latter transform is not an orthogonal transformation...

In the paper,wavelet-based adaptive support vector machine is applied to stock exchange index prediction,and Morlet wavelet function can be used as kernel function of adaptive support vector regression model. In the study, the proposed wavelet-based adaptive support vector regression models trained by the training sample sets with 2 ̃6 -dimensional input vector respectively are used to show the ...

Cai(1996b) proposed a wavelet method, BlockShrink, for estimating regression functions of unknown smoothness from noisy data by thresholding empirical wavelet co-eecients in groups rather than individually. The BlockShrink utilizes the information about neighboring wavelet coeecients and thus increases the estimation accuracy of the wavelet coeecients. In the present paper, we ooer insights int...

A new type of Wavelet Neural Network (WNN) has been proposed to enhance the function approximation and generalization performance generating an optimal size network. In the proposed WNN, the nonlinear activation function is a linear combination of wavelets that can be updated during the network training process. As a result the approximate error is significantly decreased. The RBF network based...

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function φ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function φ is compactly supported conjugate symmetric, then we prove that there exists a compactly s...