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The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real…
The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of…
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…
Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…
The scanning electron microscope (SEM) recordings of dynamic nano-electromechanical systems (NEMS) are difficult to analyze due to the noise caused by low frame rate, insufficient resolution and blurriness induced by applied electric…
Impulsive noise (IN) commonly generated by power devices can severely degrade the performance of high sensitivity wireless receivers. Accurate channel state information (CSI) knowledge is essential for designing optimal maximum a posteriori…
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin,…
Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula,…
Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
Existing learning-based denoising methods typically train models to generalize the image prior from large-scale datasets, suffering from the variability in noise distributions encountered in real-world scenarios. In this work, we propose a…
The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem, due to the non-uniqueness of the solution, and many kinds of prior information have been used to constrain it. A…
Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse…
We consider a mixed variational formulation recently proposed for the coupling of the Brinkman--Forchheimer and Darcy equations and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D version of…
This paper presents a fast computational method, the Expectation Maximization algorithm, for Maximum Likelihood (ML) estimation in diffusion tensor imaging under the Rice noise model. We further extend the ML framework to the maximum a…