Related papers: Least-Squares Method for Inverse Medium Problems

We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…

This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…

The quality of inverse problem solutions obtained through deep learning [Barbastathis et al, 2019] is limited by the nature of the priors learned from examples presented during the training phase. In the case of quantitative phase retrieval…

This paper investigates system identification problems with Gaussian inputs and quantized observations under fixed thresholds. By reinterpreting the nonlinear effects induced by quantization as the product of the unknown parameter and an…

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…

As the scale of problems and data used for experimental design, signal processing and data assimilation grow, the oft-occuring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems…

We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…

We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization. We first describe our recent theoretically guaranteed message passing algorithm that…

This paper develops a two-stage method for inference on partially identified parameters in moment inequality models with separable nuisance parameters. In the first stage, the nuisance parameters are estimated separately, and in the second…

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…

Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…

In this paper, we propose a local squared Wasserstein-2 (W_2) method to solve the inverse problem of reconstructing models with uncertain latent variables or parameters. A key advantage of our approach is that it does not require prior…

In low signal-to-noise ratio conditions, it is difficult to effectively recover the magnitude and phase information simultaneously. To address this problem, this paper proposes a two-stage algorithm to decouple the joint optimization…

Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…

Due to the COVID-19 pandemic, there is an increasing demand for portable CT machines worldwide in order to diagnose patients in a variety of settings. This has led to a need for CT image reconstruction algorithms that can produce high…

Linear regression with shuffled labels and with a noisy latent design matrix arises in many correspondence recovery problems. We propose a total least-squares approach to the problem of estimating the underlying true permutation and provide…

We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…

We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…

A two-stage batch estimation algorithm for solving a class of nonlinear, static parameter estimation problems that appear in aerospace engineering applications is proposed. It is shown how these problems can be recast into a form suitable…

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with…