The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces ...

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for the evaluation of spatially adaptive estimators and shows that the possible degree of superefficiency for minimax rate optimal estimators critically depends on...

In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that, we introduce a framework for analyzing localization aspects of window functions. Our localization theory diverges from the conventional theory in two ways. Fi...

Compressive Sensing(CS) theory can reconstruct the original images from the less measurements with using the priors of the image sparse representation. The CS theory is applied into the video super-resolution(SR) reconstruction, and a new algorithm based on wavelet transform is proposed in this paper. Firstly, wavelet transform is used to decompose the low resolution image so as to get the low ...

In this paper, an automatic text–independent Arabic word speaker identification system is presented using Fuzzy Wavelet Neural Network terminology (FWNN). The approach is combining wavelet theory to fuzzy logic and neural network which lead to fabricate a Fuzzy Wavenet . Position and dilation of the fuzzy wavenets are fixed and the weights are optimized according to learning algorithm in the ne...

Motivated by recent developments in the study of finitedimensional frames, this work develops an independent theory of finitedimensional wavelet systems on the circle. Using natural translation and dilation operators, trigonometric polynomial, orthonormal scaling functions are constructed which give rise to finite-dimensional multiresolution analyses and, consequently, orthonormal wavelet syste...

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for the evaluation of spatially adaptive estimators and shows that the possible degree of superefficiency for minimax rate optimal estimators critically depends on...

Wavelet and short-time Fourier analysis is introduced in the context of frequency decompo-sitions. Wavelet type frequency decompositions are associated with lter banks, and using thisfact, lter bank theory is used to construct multiplicity M wavelet frames and tight frames. Theway in which lter banks lead to decomposition and recomposition of arbitrary separable Hilbertspaces is...

Short term traffic forecasting has been a very important consideration in many areas of transportation research for more than 3 decades. Short-term traffic forecasting based on data driven methods is one of the most dynamic and developing research arenas with enormous published literature. In order to improve forecasting model accuracy of wavelet neural network, an adaptive particle swarm optim...