Related papers: Algorithms for Least-Squares Noncartesian MR Image…
This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas…
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…
Joint reconstruction has recently attracted a lot of attention, especially in the field of medical multi-modality imaging such as PET-MRI. Most of the developed methods rely on the comparison of image gradients, or more precisely their…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
Multi-view mesh reconstruction remains a core challenge in computer graphics and vision, especially for recovering high-frequency geometry from sparse observations. Recent methods such as 3D Gaussian Splatting (3DGS) and Neural Radiance…
We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which which suggests…
The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization…
Leverage scores have become essential in statistics and machine learning, aiding regression analysis, randomized matrix computations, and various other tasks. This paper delves into the inverse problem, aiming to recover the intrinsic model…
This paper deals with tomographic image reconstruction under the situation where some of projection data bins are contaminated with abnormal data. Such situations occur in various instances of tomography. We propose a new reconstruction…
Recent work showed neural-network-based approaches to reconstructing images from compressively sensed measurements offer significant improvements in accuracy and signal compression. Such methods can dramatically boost the capability of…
New recursive least squares algorithms with rank two updates (RLSR2) that include both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin…
This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…