Related papers: Dynamical approximation and sensor placement for f…
This paper addresses the problem of secure data reconstruction for unknown systems, where data collected from the system are susceptible to malicious manipulation. We aim to recover the real trajectory without prior knowledge of the system…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
This paper addresses the problem of optimizing sensor deployment locations to reconstruct and also predict a spatiotemporal field. A novel deep learning framework is developed to find a limited number of optimal sampling locations and based…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
The unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults and thus unknown-input reconstruction has several wide-spread applications. In this paper we…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g., limited…
The image reconstruction of chromophore concentrations using Diffuse Optical Tomography (DOT) data can be described mathematically as an ill-posed inverse problem. Recent work has shown that the use of hyperspectral DOT data, as opposed to…
A promising way to mitigate the expensive process of obtaining a high-dimensional signal is to acquire a limited number of low-dimensional measurements and solve an under-determined inverse problem by utilizing the structural prior about…
Urban transportation systems face increasing resilience challenges from extreme weather events, but current assessment methods rely on surface-level recovery indicators that miss hidden structural damage. Existing approaches cannot…