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In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise…
We propose a class of waveguides operating near cutoff such that electromagnetic energy is mainly bound to the cladding rather than the dielectric core to achieve subdiffraction confinement of light. The cladding incorporates an alternating…
Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly…
In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of…
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
Results are presented from numerical modeling of the effect of the inhomogeneity of the ion background on the complicated spatiotemporal dynamics of an electron beam with a virtual cathode in plane geometry. The possibility is demonstrated…
In recent years some attempts have been done to relate the RBF with wavelets in handling high dimensional multiscale problems. To the author's knowledge, however, the orthonormal and bi-orthogonal RBF wavelets are still missing in the…
Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient…
High-precision measurements benefit from lock-in detection of small signals. Here we discuss the extension of lock-in detection to many channels, using mutually orthogonal modulation waveforms, and show how the the choice of waveforms…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
Dimensionality reduction of ECG signals is considered within the framework of sparse representation. The approach constructs the signal model by selecting elementary components from a redundant dictionary via a greedy strategy. The proposed…
Differential microphone arrays offer a promising solution for far-field acoustic signal acquisition due to their high spatial directivity and compact array structure. A key challenge lies in designing differential beamformers that are…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…
In this paper, an algorithm based on polyphase matrix for constructing a pair of orthogonal wavelet frames is suggested, and a general form for all orthogonal tight wavelet frames on local fields of positive characteristic is described.…