Related papers: Regularizing a linearized EIT reconstruction metho…
Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct…
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…
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 purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
One-sided ultrasonic non-destructive evaluation (UNDE) is extensively used to characterize structures that need to be inspected and maintained from defects and flaws that could affect the performance of power plants, such as nuclear power…
Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned…
In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to reconstructions with significant artifacts. To overcome these…
In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests…
Ellipsoid fitting is of general interest in machine vision, such as object detection and shape approximation. Most existing approaches rely on the least-squares fitting of quadrics, minimizing the algebraic or geometric distances, with…
We discuss several methods for image reconstruction in compressed sensing photoacoustic tomography (CS-PAT). In particular, we apply the deep learning method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier. NETT: Solving Inverse…
We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
The Extreme Learning Machine (ELM) technique is a machine learning approach for constructing feed-forward neural networks with a single hidden layer and their models. The ELM model can be constructed while being trained by concurrently…
In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…
We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geometry or material parameters, we can…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…