相关论文: Differential Emission Measures from the Regularize…
Well-calibrated spectropolarimetry studies at resolutions of $R>$10,000 with signal-to-noise ratios (SNRs) better than 0.01\% across individual line profiles, are becoming common with larger aperture telescopes. Spectropolarimetric studies…
We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…
Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present…
Radiative transfer (RT) modelling is a necessary tool in the interpretation of observations of the thermal emission of interstellar dust. It is also often part of multi-physics modelling. In this context, the efficiency of radiative…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
Ring diagram analysis is a standard local helioseismic technique. Data from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) are routinely used for Ring-diagram analysis, and fits to the power spectra as…
Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…
We present observations of high temperature emission in the core of a solar active region using instruments on Hinode and SDO. These multi-instrument observations allow us to determine the distribution of plasma temperatures and follow the…
The throughout knowledge of a X-ray beam spectrum is mandatory to assess the quality of its source device. Since the techniques to directly measurement such spectra are expensive and laborious, the X-ray spectrum reconstruction using…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
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 develop a data-driven methodology based on parametric It\^{o}'s Stochastic Differential Equations (SDEs) to capture the real asymmetric dynamics of forecast errors. Our SDE framework features time-derivative tracking of the forecast,…
Regularization is a long-standing challenge for ill-posed linear inverse problems, and a prototype is the Fredholm integral equation of the first kind with additive Gaussian measurement noise. We introduce a new RKHS regularization adaptive…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…
This paper is concerned with the image reconstruction problem when the measured data are solar hard X-ray modulation profiles obtained from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI)} instrument. Our goal is to…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…