Related papers: Measure-Valued Variational Models with Application…

In this paper, we establish a Kantorovich duality for weak optimal total variation transport problems. As consequences, we recover a version of duality formula for partial optimal transports established by Caffarelli and McCann; and we also…

In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable…

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…

We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

In this paper we consider variational regularization methods for inverse problems with large noise that is in general unbounded in the image space of the forward operator. We introduce a Banach space setting that allows to define a…

Understanding the transport behavior of quantum many-body systems constitutes an important physical endeavor, both experimentally and theoretically. While a reliable classification into normal and anomalous dynamics is known to be…

In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation…

Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…

We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order…

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation…

Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to…

We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…

Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods…

This paper introduces a novel theoretical framework for the analysis of vector-valued neural networks through the development of vector-valued variation spaces, a new class of reproducing kernel Banach spaces. These spaces emerge from…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

We study an entropic optimal transport problem in which the transport plan is penalized by a nonlinear convex functional acting on the coupling. We establish existence, uniqueness, and uniform a priori bounds for minimizers, and we show…