相关论文: Applications of CGO Solutions on Coupled-Physics I…
A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the uniqueness and stability of the reconstruction of the absorption…
In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…
This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map…
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
There has been an increasing interest in utilizing machine learning methods in inverse problems and imaging. Most of the work has, however, concentrated on image reconstruction problems, and the number of studies regarding the full solution…
We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility…
The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and…
Dual-energy computed tomography (DECT) has shown great potential and promising applications in advanced imaging fields for its capabilities of material decomposition. However, image reconstructions and decompositions under sparse views…
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
Inverse scattering in optical coherence tomography (OCT) seeks to recover both structural images and intrinsic tissue optical properties, including refractive index, scattering coefficient, and anisotropy. This inverse problem is…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
Physics-guided deep learning is an important prevalent research topic in scientific machine learning, which has tremendous potential in various complex applications including science and engineering. In these applications, data is expensive…