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Article
NSNO: Neumann Series Neural Operator for Solving Helmholtz Equations in Inhomogeneous Medium
In this paper, the authors propose Neumann series neural operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation i...
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Article
Open AccessA minority of final stacks yields superior amplitude in single-particle cryo-EM
Cryogenic electron microscopy (cryo-EM) is widely used to determine near-atomic resolution structures of biological macromolecules. Due to the low signal-to-noise ratio, cryo-EM relies on averaging many images...
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Article
A second-order nonlocal approximation for Poisson model with Dirichlet boundary
In this paper, we analyze a class of nonlocal Poisson model on manifold under Dirichlet boundary condition. To get second order convergence, the geometric information of the manifold has to be incorporated in ...
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Article
Open AccessNon-line-of-sight imaging with arbitrary illumination and detection pattern
Non-line-of-sight (NLOS) imaging aims at reconstructing targets obscured from the direct line of sight. Existing NLOS imaging algorithms require dense measurements at regular grid points in a large area of the...
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Article
BI-GreenNet: Learning Green’s Functions by Boundary Integral Network
Green’s function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green’s function is difficult to compute. The tr...
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Article
Open AccessNon-line-of-sight reconstruction with signal–object collaborative regularization
Non-line-of-sight imaging aims at recovering obscured objects from multiple scattered lights. It has recently received widespread attention due to its potential applications, such as autonomous driving, rescue...
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Chapter
Low Dimensional Manifold Model in Hyperspectral Image Reconstruction
In this chapter, we present a low dimensional manifold (LDMM) for hyperspectral image reconstruction. This model is based on the observation that the spatial–spectral blocks of hyperspectral images typically...
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Article
Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold Model
In this paper we use the idea of the weighted nonlocal Laplacian (Shi et al. in J Sci Comput, 2017) to deal with the constraints in the low dimensional manifold model (Osher et al. in SIAM J Imaging Sci, 2017). I...
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Article
Weighted Nonlocal Laplacian on Interpolation from Sparse Data
Inspired by the nonlocal methods in image processing and the point integral method, we introduce a novel weighted nonlocal Laplacian method to compute a continuous interpolation function on a point cloud in hi...
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Article
Open AccessConvergence of the point integral method for Laplace–Beltrami equation on point cloud
The Laplace–Beltrami operator, a fundamental object associated with Riemannian manifolds, encodes all intrinsic geometry of manifolds and has many desirable properties. Recently, we proposed the point integral...
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Article
A two-level method for sparse time-frequency representation of multiscale data
Based on the recently developed data-driven time-frequency analysis (Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level m...
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Article
Sparse time-frequency representation of nonlinear and nonstationary data
Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency an...
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Article
A decadal microwave record of tropical air temperature from AMSU-A/aqua observations
Atmospheric temperature is one of the most important climate variables. This observational study presents detailed descriptions of the temperature variability imprinted in the 9-year brightness temperature dat...
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Article
On Singularity Formation of a Nonlinear Nonlocal System
We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei (Comm Pure Appl Math ...
