Related papers: Calculating Spectra by Sequential High-Pass Filter…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…
Accurate time series analysis is essential for studying variable astronomical sources, where detecting periodicities and characterizing power spectral density (PSD) are crucial. The Lomb-Scargle periodogram, commonly used in astronomy for…
Deep learning models extract, before a final classification layer, features or patterns which are key for their unprecedented advantageous performance. However, the process of complex nonlinear feature extraction is not well understood, a…
We introduce the concept of `hyperpixels' in which each element of a pixel filter array (suitable for CMOS image sensor integration) has a spectral transmission tailored to a target spectral component expected in application-specific…
In this article, we propose a spectral method for a class of multivariate inhomogeneous spatial point processes, namely the second-order intensity reweighted stationary processes. A key ingredient of our approach is utilizing the asymptotic…
The requirements to achieve high detection efficiency (above 50\%) and gigahertz (GHz) frame rate for the proposed 42-keV X-ray free-electron laser (XFEL) at Los Alamos are summarized. Direct detection scenarios using C (diamond), Si, Ge…
Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher…
Hyperuniform structures possess the ability to confine and drive light, although their fabrication is extremely challenging. Here we demonstrate that speckle patters obtained by a superposition of randomly arranged sources of Bessel beams…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
The reflectionless filter cell described in this article alleviates many system problems associated with excess out-of-band gain, impedance mismatches, and component interactions. The simplest filter cell exhibits a third-order Inverse…
All spectrometers rely on some mechanism to achieve spectral selectivity; common examples include gratings, prisms, and interferometers with moving mirrors. We experimentally demonstrated and validated a spectroscopic technique -- here…
Kernel phase interferometry (KPI) is a data processing technique that allows for the detection of asymmetries (such as companions or disks) in high-Strehl images, close to and within the classical diffraction limit. We show that KPI can…
Let $L$ be the $n$-th order linear differential operator $Ly = \phi_0y^{(n)} + \phi_1y^{(n-1)} + \cdots + \phi_ny$ with variable coefficients. A representation is given for $n$ linearly independent solutions of $Ly=\lambda r y$ as power…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
Indoor image features extraction is a fundamental problem in multiple fields such as image processing, pattern recognition, robotics and so on. Nevertheless, most of the existing feature extraction methods, which extract features based on…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Hyperspectral imaging offers detailed spectral information for mineral mapping; however, weak mineral signatures are often masked by noisy and redundant bands, limiting detection performance. To address this, we propose a two-stage…
Particle-in-cell (PIC) simulations of relativistic shocks are in principle capable of predicting the spectra of photons that are radiated incoherently by the accelerated particles. The most direct method evaluates the spectrum using the…
We study the problem of the appropriate choice of the interpolating kernel to be used in the evaluation of gradients of functions. Such interpolation technique is often used in applications, e.g. it is typical for Smoothed Particle…