Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coefficients. However, it has been shown that grouping the empirical wavelet coefficients into blocks and making simultaneous threshold decisions about all the coefficients in each block has a number of advantages over term-by-term wavelet thresholding, includ...

In wavelet representations, the magnitude of the wavelet coeecients depends on both the smoothness of the represented function f and on the wavelet. We investigate the extreme values of wavelet coeecients for the standard function spaces A k = ff j kf (k) k 2 1g, k 2 N. In particular, we compare two important families of wavelets in this respect, the orthonormal Daubechies wavelets and the semi...

In this paper, those splendid characters of the Hilbert transform let the processes that taking wavelet transform after taking Hilbert transform for the statistic self-similarity processes FBM [ ) (t BH ] become another processes, that firstly taking Hilbert transform for the wavelet function ) (t φ and forming a new wavelet function ) (t ψ , secondly taking the wavelet transform for ) (t BH . ...

A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a tran...

This paper proposes a wavelet neural network (WNN) for SAR image segmentation by combining the wavelet transform and an artificial neural network. The WNN combines the multiscale analysis ability of the wavelet transform and the classification capability of the artificial neural network by setting the wavelet function as the transfer function of the neural network. Several SAR images are segmen...

This paper presents a new method for shift keying using the combination of scaling function and wavelet named scaling wavelet shift keying (SWSK). An algorithm for SWSK modulation is carried out where the scaling function and the wavelet are encoded to 1 and 0 in accordance with the binary input, respectively. Signal energy, correlation coefficient and error probability of SWSK are derived from...

An improved Differential Evolution (DE) that incorporates wavelet-based mutation and crossover operations is proposed. In the mutation operation, the scaling factor is controlled by a wavelet function. In the crossover operation, the trial population vectors are modified by a wavelet function. The wavelet theory applied is to enhance DE in exploring the solution space more effectively for a bet...

We present a new method for the reduction of noise in images, using a wavelet transform. The method relies on two principles. The rst is the characterization of the local function regularity by wavelet coeecients. The second is an a priori, geometrical model for wavelet coeecients. Both are combined in a Bayesian framework, to compute for each wavelet coeecient the probability of being \suu-cie...

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of theminimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept ofminimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Se...

This paper describes a new method for constructing wavelet neural network in order to improve the accuracy of prediction for multi-dimensional function spaces. An algorithm is developed using the concept of evolutionary search in wavelet neural network. It helps in decreasing the computational effort needed for building the wavelet neural network. Several modifications to wavelet neural network...