Related papers: A polarization tensor approximation for the Hessia…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin…
We introduce templates for exponential asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in classes of linear and nonlinear equations that are singularly…
The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…
This study presents a frequency-domain, Hessian-free ray-Born inversion method for quantitative ultrasound tomography, extending the author's previous Hessian-based approach. Both approaches model acoustic wave propagation using a ray-based…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
We develop a highly accurate analytic approximation for small-scale non-cold relic perturbations by solving the collisionless Boltzmann equation in the quasi-stationary regime. The approximation is implemented in CLASSIER (CLASS Integral…
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…
Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…