Inverse problems deal with the quest for unknown causes of observed consequences,
based on predictive models, known as the forward models, that associate the former …

Electrical impedance tomography (EIT) is developed to investigate the internal conductivity
changes of an object through a series of boundary electrodes, and has become increasingly …

Solving inverse problems with sparsity promoting regularizing penalties can be recast in the
Bayesian framework as finding a maximum a posteriori (MAP) estimate with sparsity …

Sparse recovery seeks to estimate the support and the non-zero entries of a sparse signal
from possibly incomplete noisy observations, with,. It has been shown that under various …

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 …

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 …

A recently proposed iterated alternating sequential (IAS) MEG inverse solver algorithm,
based on the coupling of a hierarchical Bayesian model with computationally efficient Krylov …

Dictionary learning, aiming at representing a signal in terms of the atoms of a dictionary, has
gained popularity in a wide range of applications, including, but not limited to, image …