Related papers: On the use of continuous wavelet analysis for moda…
Cloud detection is a specialized application of image recognition and object detection using remotely sensed data. The task presents a number of challenges, including analyzing images obtained in visible, infrared and multi-spectral…
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…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
A formalism is derived to analyze the scattering of a conducting structure based on the characteristic modes of another structure whose surface is a superset of the first structure. This enables the analysis and comparison of different…
Masked Image Modeling (MIM) has garnered significant attention in self-supervised learning, thanks to its impressive capacity to learn scalable visual representations tailored for downstream tasks. However, images inherently contain…
The physical pictures of eigen-mode theory (EMT) and the conventional characteristic mode theory (CMT) reveal a fact that: the EMT and CMT are the modal theories for electromagnetic wave-guiding and scattering (for details, please see the…
Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for…
The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…
I investigate the scattering properties of transformation devices as the traditional impedance matching criteria are altered. This is demonstrated using simple theory and augmented by numerical simulations that investigate the role of…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…
Radar-based materials detection received significant attention in recent years for its potential inclusion in consumer and industrial applications like object recognition for grasping and manufacturing quality assurance and control. Several…
Smartphones consist of different sensors, which provide a platform for data acquisition in many scientific researches such as driving style identification systems. In the present paper, smartphone data are used to evaluate the driving…
Biomedical signal processing extract meaningful information from physiological signals like electrocardiograms (ECGs), electroencephalograms (EEGs), and electromyograms (EMGs) to diagnose, monitor, and treat medical conditions and diseases…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
Multimodal datasets, where measurements are obtained from multiple sensors, have become central to many scientific domains. In unsupervised settings, most representation learning methods focus on identifying shared latent structures, such…
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…