Related papers: Probabilistic Regularization in Inverse Optical Im…

Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the…

In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…

We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…

We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors…

This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or…

Restore lost images due to noise and blurred is a burgeoning subject in image processing and despite the different algorithms on this subject, but the effort to improve is always considered. The definition of fractional derivatives in…

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…

We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from…

We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…

The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…

Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…

Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…