Related papers: Bias and Multiscale Correction Methods for Variati…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

Neural networks produced by standard training are known to suffer from poor accuracy on rare subgroups despite achieving high accuracy on average, due to the correlations between certain spurious features and labels. Previous approaches…

Wind speed at sea surface is a key quantity for a variety of scientific applications and human activities. Due to the non-linearity of the phenomenon, a complete description of such variable is made infeasible on both the small scale and…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…

Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…

In this paper, we address the problem of stabilization in continuous time linear dynamical systems using state feedback when compressive sampling techniques are used for state measurement and reconstruction. In [5], we had introduced the…

Time series data from observations of black hole ringdown gravitational waves are often analyzed in the time domain by using damped sinusoid models with acyclic boundary conditions. Data conditioning operations, including downsampling,…

A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…

Noise bias is a significant source of systematic error in weak gravitational lensing measurements that must be corrected to satisfy the stringent standards of modern imaging surveys in the era of precision cosmology. This paper reviews the…

In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses;…

Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…

One of the primary sources of suboptimal image quality in ultrasound imaging is phase aberration. It is caused by spatial changes in sound speed over a heterogeneous medium, which disturbs the transmitted waves and prevents coherent…

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

We solve a weakly supervised regression problem. Under "weakly" we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack…

Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…

We present a novel method for inferring ground-truth signal from multiple degraded signals, affected by different amounts of sensor exposure. The algorithm learns a multiplicative degradation effect by performing iterative corrections of…

We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish…

This paper proposes an extension to the classical 3D variational data assimilation approach by explicitly incorporating as a prior information, the transform-domain sparsity observed in a large class of geophysical signals. In particular,…