Related papers: On the Realization and Analysis of Circular Harmon…
Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…
A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response…
Second harmonic generation (SHG) microscopy is a valuable tool for optical microscopy. SHG microscopy is normally performed as a point scanning imaging method, which lacks phase information and is limited in spatial resolution by the…
Sensitive measurements of the linearly polarized spectra of stars can be used to deduce geometric properties of their otherwise unresolved circumstellar environments. This paper describes some of the evidence for optical pumping and…
Astronomical polarimetry is a powerful technique that can provide physical information sometimes difficult or impossible to obtain by any other type of observation. Almost every class of binary star can benefit from polarimetric…
Spectrogram-based representations have grown to dominate the feature space for deep learning audio analysis systems, and are often adopted for speech analysis also. Initially, the primary motivator for spectrogram-based representations was…
Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group $G$ on a finite set $X$ to a graded action of $G$ on a polynomial ring quotient by viewing $X$ as a $G$-stable point…
As a basic optical element, circular polarizer plays significant roles in signal transmission, measurements and life science microscopy. Three-dimensional (3D) chiral structures have been thought to be necessary to realize circular…
We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic…
We demonstrate synthesis of super-octave-spanning and phase-locked transients in the multi-terahertz frequency range with amplitudes exceeding 13 MV/cm. Sub-cycle polar asymmetry of the electric field is adjusted by changing the relative…
Sensing light's polarization and wavefront direction enables surface curvature assessment, material identification, shadow differentiation, and improved image quality in turbid environments. Traditional polarization cameras utilize multiple…
A compact and broadband polarimetric imaging platform is presented, based on second-harmonic generation (SHG) in nonlinear flat-optics. The system employs periodic all-dielectric AlGaAs gratings to induce polarization-dependent SH emission,…
Speckle patterns observed in coherent optical imaging reflect important characteristic information of the scattering object. To capture speckle patterns, angular resolved or oblique illumination geometries are usually employed in…
One of the biggest challenges of acoustic scene classification (ASC) is to find proper features to better represent and characterize environmental sounds. Environmental sounds generally involve more sound sources while exhibiting less…
We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
The commonly used radial distortion model for camera calibration is in fact an assumption or a restriction. In practice, camera distortion could happen in a general geometrical manner that is not limited to the radial sense. This paper…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…