相关论文: Applications of CGO Solutions on Coupled-Physics I…

This is the manuscript of the chapter for a planned Handbook of Mathematical Methods in Imaging that surveys the mathematical models, problems, and algorithms of the Thermoacoustic (TAT) and Photoacoustic (PAT) Tomography. TAT and PAT…

Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT measurement setup, the used…

Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…

Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…

The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time,…

Learning physics-constrained inverse operators-rather than post-processing physics-based reconstructions-is a broadly applicable strategy for problems with expensive forward models. We demonstrate this principle in three-dimensional…

We use thermal noise induced currents to image the real and imaginary parts of the conductivity of a body. Covariances of the thermal noise currents measured at a few electrodes are shown to be related to a deterministic problem. We use the…

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the…

ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging technique whose inverse problem can be formulated as an initial condition reconstruction. In this paper, we introduce a new algorithm originally designed to…

This user manual is intended to provide a detailed description on model-based optimization for imaging inverse problem. Theseproblems can be particularly complex and challenging, especially for individuals without prior exposure to convex…

This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider…

Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…

Researchers familiar with the state of the art are aware that the development of close-formed solutions for the EIT problem was not able to overpass the case of once-time differentiable conductivities beside the well known particular…

This paper focuses on the acousto-electromagnetic tomography, a recently introduced hybrid imaging technique. In a previous work, the reconstruction of the electric permittivity of the medium from internal data was achieved under the Born…

Since most inverse problems arising in scientific and engineering applications are ill-posed, prior information about the solution space is incorporated, typically through regularization, to establish a well-posed problem with a unique…

The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation…

We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

In this paper we provide a mathematical model for imaging an anisotropic, orthotropic medium with Polarization-Sensitive Optical Coherence Tomography (PS-OCT). The imaging problem is formulated as an inverse scattering problem in three…