Related papers: On a Dynamic Variant of the Iteratively Regularize…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
In this work, we propose a deep learning-based imaging method for addressing the multi-frequency electromagnetic (EM) inverse scattering problem (ISP). By combining deep learning technology with EM physical laws, we have successfully…
We investigate generalized versions of the Iteratively Regularized Landweber Method, initially introduced in [Appl. Math. Optim., 38(1):45-68, 1998], to address linear and nonlinear ill-posed problems. Our approach is inspired by the…
In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
This paper examines inverse Cauchy problems that are governed by a kind of elliptic partial differential equation. The inverse problems involve recovering the missing data on an inaccessible boundary from the measured data on an accessible…
We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
This study introduces an iterative Bayesian Robbins--Monro (IBRM) sequence, which unites the classical Robbins--Monro sequence with statistical estimation for faster root-finding under noisy observations. Although the standard…
In this paper we propose a real-time and robust solution to large-scale multiple rotation averaging. Until recently, Multiple rotation averaging problem had been solved using conventional iterative optimization algorithms. Such methods…
Graph Neural Networks (GNNs) have achieved remarkable performance in a wide range of graph-related learning tasks. However, explaining their predictions remains a challenging problem, especially due to the mismatch between the graphs used…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data…
Heart rate variability (HRV) analysis is important for the assessment of autonomic cardiovascular regulation. The inverse Gaussian process (IGP) has been widely used for beat-to-beat HRV modeling, as it gives a physiological relevant…