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We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…

We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…

Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new…

This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…

To achieve point cloud denoising, traditional methods heavily rely on geometric priors, and most learning-based approaches suffer from outliers and loss of details. Recently, the gradient-based method was proposed to estimate the gradient…

Pose estimation is a general problem in computer vision with wide applications. The relative orientation of a 3D reference object can be determined from a 3D rotated version of that object, or from a projection of the rotated object to a 2D…

We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…

High-quality point cloud data is a critical foundation for tasks such as autonomous driving and 3D reconstruction. However, LiDAR-based point cloud acquisition is often affected by various disturbances, resulting in a large number of noise…

Registration of 3D point clouds is a fundamental task in several applications of robotics and computer vision. While registration methods such as iterative closest point and variants are very popular, they are only locally optimal. There…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…

This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…

In this paper, we present IRON (Invariant-based global Robust estimation and OptimizatioN), a non-minimal and highly robust solution for point cloud registration with a great number of outliers among the correspondences. To realize this, we…

Point cloud filtering, the main bottleneck of which is removing noise (outliers) while preserving geometric features, is a fundamental problem in 3D field. The two-step schemes involving normal estimation and position update have been shown…

Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…