Related papers: LS-Net: Learning to Solve Nonlinear Least Squares …
We consider the simultaneous deblurring of a set of noisy images whose point spread functions are different but known and spatially invariant, and the noise is Gaussian. Currently available iterative algorithms that are typically used for…
Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but…
We present GLNet, a self-supervised framework for learning depth, optical flow, camera pose and intrinsic parameters from monocular video - addressing the difficulty of acquiring realistic ground-truth for such tasks. We propose three…
We propose a learning-based method that solves monocular stereo and can be extended to fuse depth information from multiple target frames. Given two unconstrained images from a monocular camera with known intrinsic calibration, our network…
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…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…
Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…
In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE's) with either (or both) L2 or point-wise bounded…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Monocular depth estimation is a highly challenging problem that is often addressed with deep neural networks. While these are able to use recognition of image features to predict reasonably looking depth maps the result often has low metric…
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally…
An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the…
Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
This article focuses on solving parametric transmission problems in one and two spatial dimensions. These problems belong to a class of partial differential equations that arise in the modeling of physical systems with heterogeneous…
Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…
In this paper, we propose a sparse least squares (SLS) optimization model for solving multilinear equations, in which the sparsity constraint on the solutions can effectively reduce storage and computation costs. By employing variational…
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…
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…