We review the current state-of-the-art of diffuse optical imaging, which is an emerging
technique for functional imaging of biological tissue. It involves generating images using …

In the literature on regularization, many different parameter choice methods have been
proposed in both deterministic and stochastic settings. However, based on the available …

Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at
New Mexico Tech and is designed to be accessible to typical graduate students in the …

Atmospheric CO 2 inversions estimate surface carbon fluxes from an optimal fit to
atmospheric CO 2 measurements, usually including prior constraints on the flux estimates …

We present a reformulation of the Bayesian approach to inverse problems, that seeks to
accelerate Bayesian inference by using polynomial chaos (PC) expansions to represent …

We consider a Bayesian approach to nonlinear inverse problems in which the unknown
quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior …

Characterizing statistical properties of solutions of inverse problems is essential in many
applications, and in particular those that involve uncertainty quantification. Bayesian …

Although numerical approximation and statistical inference are traditionally covered as
entirely separate subjects, they are intimately connected through the common purpose of …

We present an efficient numerical strategy for the Bayesian solution of inverse problems.
Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to …

Inverse heat conduction problems (IHCPs) are problems of estimating unknown quantities of
interest (QoIs) of the heat conduction with given temperature observations. The challenge of …