Related papers: Sparse Source Identification in Transient Advectio…
In groundwater contaminant remediation and risk assessment, it is important to identify parameters of the contaminant source and hydraulic conductivity field by solving an inverse problem. However, if the dimensionality of the inverse…
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…
A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…
Solving storage problem: where objects must be accurately placed into containers with precise orientations and positions, presents a distinct challenge that extends beyond traditional rearrangement tasks. These challenges are primarily due…
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration,…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
The Pathfinder of the Type-A satellites in the Chasing All Transients Constellation Hunters (CATCH) space mission is equipped with Micro-Pore Optics (MPOs) and four single-pixel Silicon Drift Detectors (SDDs). Due to the lack of position…
We propose a joint channel estimation and data detection algorithm for massive multilple-input multiple-output systems based on diffusion models. Our proposed method solves the blind inverse problem by sampling from the joint posterior…
This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in…
We study the nonlinear inverse source problem of detecting, localizing and identifying unknown accidental disturbances on forced and damped transmission networks. A first result is that strategic observation sets are enough to guarantee…
We perform an exhaustive study of the simplest, nontrivial problem in advection-diffusion -- a finite absorber of arbitrary cross section in a steady two-dimensional potential flow of concentrated fluid. This classical problem has been…
We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Firstly, we extend the Ambient Diffusion framework to enable training directly from measurements corrupted in the Fourier…
Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
Missions such as WMAP or Planck measure full-sky fluctuations of the cosmic microwave background and foregrounds, among which bright compact source emissions cover a significant fraction of the sky. To accurately estimate the diffuse…
We consider a problem of identification of point sources in time dependent advection-diffusion systems with a non-linear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of non-linear…
We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both…
Radio frequency sources are observed at a fusion center via sensor measurements made over slow flat-fading channels. The number of sources may be larger than the number of sensors, but their activity is sparse and intermittent with bursty…
We study the inference of the origin and the pattern of contamination in water distribution networks. We assume a simplified model for the dyanmics of the contamination spread inside a water distribution network, and assume that at some…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…