Related papers: Convergence rates under a range invariance conditi…
We study the construction and updating of spectral preconditioners for regularized Newton methods and their application to electromagnetic inverse medium scattering problems. Moreover, we show how a Lepski\u{i}-type stopping rule can be…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
An inverse scattering problem for SAR data in application to through-the-wall imaging is addressed. In contrast with the conventional algorithms of SAR imaging, that work with the linearized mathematical model based on the Born…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
The contrast source inversion (CSI) method and the subspace-based optimization method (SOM) are first proposed in 1997 and 2009, respectively, and subsequently modified. The two methods and their variants share several properties and thus…
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…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
Variational auto-encoders (VAEs) are a powerful approach to unsupervised learning. They enable scalable approximate posterior inference in latent-variable models using variational inference (VI). A VAE posits a variational family…
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…
We combine conditional variational autoencoders (VAE) with adversarial censoring in order to learn invariant representations that are disentangled from nuisance/sensitive variations. In this method, an adversarial network attempts to…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
This work extends the results of [Garde and Hyv\"onen, Math. Comp. 91:1925-1953] on series reversion for Calder\'on's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and…
Variational inequalities are a broad formalism that encompasses a vast number of applications. Motivated by applications in machine learning and beyond, stochastic methods are of great importance. In this paper we consider the problem of…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…