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Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms.…
For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the…
Spectral-spatial processing has been increasingly explored in remote sensing hyperspectral image classification. While extensive studies have focused on developing methods to improve the classification accuracy, experimental setting and…
In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…
The bundle of geometry and appearance in computer vision has proven to be a promising solution for robots across a wide variety of applications. Stereo cameras and RGB-D sensors are widely used to realise fast 3D reconstruction and…
Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…
Some novel numerical approaches to solving direct and inverse obstacle scattering problems (IOSP) are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is…
Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
We introduce an inexact variant of Stochastic Mirror Descent (SMD), called Inexact Stochastic Mirror Descent (ISMD), to solve nonlinear two-stage stochastic programs where the second stage problem has linear and nonlinear coupling…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
We consider the problem of reconstructing an unknown function $u\in L^2(D,\mu)$ from its evaluations at given sampling points $x^1,\dots,x^m\in D$, where $D\subset \mathbb R^d$ is a general domain and $\mu$ a probability measure. The…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
Managing the dynamic regions in the photometric loss formulation has been a main issue for handling the self-supervised depth estimation problem. Most previous methods have alleviated this issue by removing the dynamic regions in the…
A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training…
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…