We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0, 3]. We compare these spaces and characterize them in terms of Daubechies wavelets.

Wavelet theory has been extensively developed in the function space L2 and discrete wavelet transform has successful applications in many areas. However, to understand better the performance of different discrete wavelet transforms, it is important to investigate their underlying discrete wavelet systems in l2. Though some preliminary results have been found recently, despite the fact that stab...

In this paper, we propose an image restoration algorithm based on state-of-the-art wavelet domain statistical models. We present an efficient method to estimate the model parameters from the observations, and solve the restoration problem in orthonormal and translation–invariant (TI) wavelet domains. Substantial improvements over previous wavelet–based restoration methods are obtained. The use ...

In this paper, we introduce a novel approach to estimate the illumination and reflectance of an image. The approach is based on illumination-reflectance model and wavelet theory. We use a homomorphic wavelet filter (HWF) and define a wavelet quotient image (WQI) model based on dyadic wavelet transform. The illumination and reflectance components are estimated by using HWF and WQI, respectively....

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...

The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the...

An application of Beta wavelet networks to synthesize pass-high and pass-low wavelet filters is investigated in this work. A Beta wavelet network is constructed using a parametric function called Beta function in order to resolve some nonlinear approximation problem. We combine the filter design theory with wavelet network approximation to synthesize perfect filter reconstruction. The order fil...

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-based filterbank. By allowing for slight redundancy, we obtain the Marr wavelet pyramid decomposition that features improved translation-invari...