We propose an efficient probabilistic method to solve a fully deterministic problem—we
present a randomized optimization approach that drastically reduces the enormous …

The discrete empirical interpolation method (DEIM) is a popular technique for nonlinear
model reduction, and it has two main ingredients: an interpolating basis that is computed …

We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method
addressing the restoration and reconstruction of piecewise constant objects. Our key …

Abstract Markov chain Monte Carlo (MCMC) approaches are traditionally used for
uncertainty quantification in inverse problems where the physics of the underlying sensor …

Nonlinear parametric inverse problems appear in many applications. Here, we focus on
diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest …

( ) ∫ Page 1 Applied Mathematics and Nonlinear Sciences, 9(1) (2024) 1-25 Applied
Mathematics and Nonlinear Sciences https://www.sciendo.com †Corresponding author. Email …

Nonlinear parametric inverse problems appear in many applications and are typically very
expensive to solve, especially if they involve many measurements. These problems pose …

For parameter inversion problems governed by systems of partial differential equations,
such as those arising in Diffuse Optical Tomography (DOT), even the cost of repeated …

Nonlinear inverse problems appear in many applications for identification and localization of
anomalous regions, such as finding tumors in the body, luggage screening, and finding …