The inverse problem of synthetic aperture interferometric radiometers (SAIRs) aims at retrieving the brightness temperature map from visibility function samples. To efficiently obtain an accurate solution, accelerated iterative regularization technique is proposed to reconstruct SAIR map. acceleration modifies conventional least square using a negative penalty term speed up initial iterations. ...

In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The is based on well known iteratively regularized Landweber iteration together with an extrapolation strategy. general formulation of excludes use certain functions such as total variation like penalty functionals, $L^1$ etc. scheme presented pap...

With the development of in-vivo free-space fluorescence molecular imaging and multi-modality imaging for small animals, there is a need for new reconstruction methods for real animal-shape models with a large dataset. In this paper we are reporting a novel hybrid adaptive finite element algorithm for fluorescence tomography reconstruction, based on a linear scheme. Two different inversion strat...

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an ill-posed linear inverse problem with an unknown but estimab...

The paper investigates a nonparametric regression method based on smoothing spline analysis of variance (ANOVA) approach to address the problem of global sensitivity analysis (GSA) of complex and computationally demanding computer codes. The two steps algorithm of this method involves an estimation procedure and a variable selection. The latter can become computationally demanding when dealing ...

In this paper, we study a family of gradient descent algorithms to approximate the regression function from Reproducing Kernel Hilbert Spaces (RKHSs), the family being characterized by a polynomial decreasing rate of step sizes (or learning rate). By solving a bias-variance trade-off we obtain an early stopping rule and some probabilistic upper bounds for the convergence of the algorithms. Thes...

The present paper explores the link between thresholding, one of the key enablers in sparsity-promoting algorithms, and Volterra system identification in the context of time-adaptive or online learning. A connection is established between the recently developed generalized thresholding operator and optimization theory via the concept of proximal mappings which are associated with non-convex pen...