Related papers: Focusing inversion techniques applied to electrica…
SUMMARY Geophysical imaging using the inversion procedure is a powerful tool for the exploration of the Earth's subsurface. However, the interpretation of inverted images can sometimes be difficult, due to the inherent limitations of…
Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…
This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…
In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected…
This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
Several regularization methods have recently been introduced which force the latent activations of an autoencoder or deep neural network to conform to either a Gaussian or hyperspherical distribution, or to minimize the implicit rank of the…
In electrical impedance tomography, algorithms based on minimizing the linearized-data-fit residuum have been widely used due to their real-time implementation and satisfactory reconstructed images. However, the resulting images usually…
Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…
Multi-energy computed tomography (ME-CT) is an x-ray transmission imaging technique that uses the energy dependence of x-ray photon attenuation to determine the elemental composition of an object of interest. Mathematically, forward ME-CT…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…
Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…
We study the multi-reference alignment (MRA) problem of recovering a signal from noisy observations acted on by unknown random circular shifts. While the information-theoretic limits of MRA are well characterized in many settings, the…
Inversion of electromagnetic data finds applications in many areas of geophysics. The inverse problem is commonly solved with either deterministic optimization methods (such as the nonlinear conjugate gradient or Gauss-Newton) which are…
The instability of embedding spaces across model retraining cycles presents significant challenges to downstream applications using user or item embeddings derived from recommendation systems as input features. This paper introduces a novel…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…