This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

In the field of biomedical image reconstruction, functional near infra-red spectroscopy
(fNIRs) is a promising technology that uses near infra-red light for non-invasive imaging and …

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-
posed. Imaging methods typically address this difficulty by regularizing the estimation …

Fifteen years ago, when the idea of using probability to model unknown parameters to be
estimated computationally was a less commonly accepted idea than it is today, writing a …

Bayesian hierarchical models have been demonstrated to provide efficient algorithms for
finding sparse solutions to ill-posed inverse problems. The models comprise typically a …

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet
challenging task. While methods such as compressive sensing have demonstrated high …

The recovery of sparse generative models from few noisy measurements is an important and
challenging problem. Many deterministic algorithms rely on some form of \ell_1-\ell_2 …

This paper introduces a computational framework to incorporate flexible regularization
techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed …

Dictionary learning methods continue to gain popularity for the solution of challenging
inverse problems. In the dictionary learning approach, the computational forward model is …

This paper develops a new empirical Bayesian inference algorithm for solving a linear
inverse problem given multiple measurement vectors of noisy observable data. Specifically …