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Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…
In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely…
We propose a new technique for the detection of single atoms in ultracold quantum gases. The technique is based on scanning electron microscopy and employs the electron impact ionization of trapped atoms with a focussed electron probe.…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
Epilepsy is one of the most common and yet diverse set of chronic neurological disorders. This excessive or synchronous neuronal activity is termed seizure. Electroencephalogram signal processing plays a significant role in detection and…
Electric field measurement in plasmas permits quantitative comparison between the experiment and the simulation in this study. An electro-optic (EO) sensor based on Pockels effect is demonstrated to measure wave electric fields in the…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
Weak gravitational lensing provides a unique method to directly measure the distribution of mass in the universe. Because the distortions induced by lensing in the shape of background galaxies are small, the measurement of weak lensing…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
The detection of power-laws in real data is a demanding task for several reasons. The two, more frequently met, being: (i) real data possess noise which affects significantly the power-law tails and (ii) there is no solid tool for the…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
Wavefront sensing from an extended object is a challenging task since the phase to be sensed is disturbed by the phase generated from the structure of the extended object. To address this problem, a general wavefront sensor was proposed.…
We present a new method of wavelet packet decomposition to be used in gravitational wave detection. An issue in wavelet analysis is what is the time-frequency resolution which is best suited to analyze data when in quest of a signal of…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
Defects in crystalline materials control the properties of materials, and their characterization focuses our strategies to optimize performance. Electron microscopy has served as the backbone of our understanding of defect structure and…
We present a numerical method to model electric field sensitive scanning probe microscopy measurements which allows for a tip of arbtrary shape and invokes image charges to exactly account for a sample dielectric overlayer. The method is…
We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…
We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and a nonlinear feedback…
Matching a wavelet to class of signals can be of interest in feature detection and classification based on wavelet representation. The aim of this work is to provide a quantitative approach to the problem of matching a wavelet to…
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…