Related papers: Point spread function approximation of high rank H…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
Accessing the point-spread function (PSF) of a complex optical system is important for a variety of imaging applications. However, placing an invasive point source is often impractical, and estimating it blindly with multiple frames is slow…
This paper presents CSST-PSFNet, a deep learning method for high-fidelity point spread function (PSF) reconstruction developed for the Chinese Space Station Survey Telescope (CSST). The model integrates a residual neural network, a…
Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an…
We introduce a scheme for probabilistic hypocenter inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation.…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
This paper is concerned with the approximations of random dispersal operators/equations by nonlocal dispersal operators/equations. It first proves that the solutions of properly rescaled nonlocal dispersal initial-boundary value problems…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
A simultaneously transmitting and reflecting surface (STARS) assisted near-field (NF) integrated sensing and communication (ISAC) framework is proposed, where the radio sensors are installed on the STARS to directly conduct the…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…
Implicit Processes (IPs) represent a flexible framework that can be used to describe a wide variety of models, from Bayesian neural networks, neural samplers and data generators to many others. IPs also allow for approximate inference in…
Accurate astrometry and photometry of saturated and coronagraphic point spread functions (PSFs) are fundamental to both ground- and space-based high contrast imaging projects. For ground-based adaptive optics imaging, differential…
The concept of dispatchable region is useful in quantifying how much renewable generation power the system can handle. In this paper, we aim to provide an improved dispatchable region approximation method in distribution networks. First,…
The Chinese Space Station Survey Telescope (CSST) presents significant potential for high-precision astrometry. In this study, we show that the point spread function (PSF) modeled by the discrete PSF with Multi-Gaussian function can…
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…
Point-spread function of the probe forming optics ($PSF_{optics} $) is reported for the first time in an uncorrected (without multipole correctors) scanning electron microscope (SEM). In an SEM, the electron probe information is lost as the…