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Discrete wavelet transform of finite-length signals must necessarily handle the signal boundaries. The state-of-the-art approaches treat such boundaries in a complicated and inflexible way, using special prolog or epilog phases. This holds…
Unidirectional optical systems enable selective control of light through asymmetric processing of radiation, effectively transmitting light in one direction while blocking unwanted propagation in the opposite direction. Here, we introduce a…
Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by…
Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from…
Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…
We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than…
Delay-Doppler multiplexing has recently stirred a great deal of attention in research community. While multiple studies have investigated pulse-shaping aspects of this technology, it is challenging to identify the relationships between…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
We derive equations of motion for bivariational wave functions with orthogonal adaptive basis sets and specialize the formalism to the coupled cluster ansatz. The equations are related to the biorthogonal case in a transparent way, and…
Order-independent transparency schemes rely on low-order approximations of transmittance as a function of depth. We introduce a new wavelet representation of this function and an algorithm for building and evaluating it efficiently on a…
We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion…
The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a…
With the growth of digital networks such as the Internet, digital media have been explosively developed in e-commerce and online services. This causes problems such as illegal copy and fake ownership. Watermarking is proposed as one of the…
The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for…
In this paper, we give a parameterization of the class of bivariate symmetric orthonormal scaling functions with filter size $6\times 6$ using the standard dilation matrix 2I. In addition, we give two families of refinable functions which…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
An algorithm is described that can generate random variants of a time series or image while preserving the probability distribution of original values and the pointwise Holder regularity. Thus, it preserves the multifractal properties of…
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…