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Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…

Numerical Analysis · Mathematics 2026-01-28 Weiwei Xu , Weijie Shen , Zhengjian Bai , Chen Xu

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

Optimization and Control · Mathematics 2011-08-09 Venkat Chandrasekaran , Sujay Sanghavi , Pablo A. Parrilo , Alan S. Willsky

Trendy suggestions for learning-based elastic warps enable the deep image stitchings to align images exposed to large parallax errors. Despite the remarkable alignments, the methods struggle with occasional holes or discontinuity between…

Computer Vision and Pattern Recognition · Computer Science 2023-12-27 Minsu Kim , Yongjun Lee , Woo Kyoung Han , Kyong Hwan Jin

Multi-image alignment, bringing a group of images into common register, is an ubiquitous problem and the first step of many applications in a wide variety of domains. As a result, a great amount of effort is being invested in developing…

Image and Video Processing · Electrical Eng. & Systems 2018-02-12 Cecilia Aguerrebere , Mauricio Delbracio , Alberto Bartesaghi , Guillermo Sapiro

We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to…

Optimization and Control · Mathematics 2021-01-20 Derek Driggs , Junqi Tang , Jingwei Liang , Mike Davies , Carola-Bibiane Schönlieb

Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…

Statistics Theory · Mathematics 2023-05-30 Hang Yu , Zhenxing Dou , Zhiwei Chen , Xiaomeng Yan

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

Optimization and Control · Mathematics 2026-05-26 Bogdan K. Jastrzębski , Radosław Pytlak

We present an algorithmic contribution to improve the efficiency of robust trim-fitting in outlier affected geometric regression problems. The method heavily relies on the quick sort algorithm, and we present two important insights. First,…

Computer Vision and Pattern Recognition · Computer Science 2022-09-07 Min Li , Laurent Kneip

Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for…

Optimization and Control · Mathematics 2023-11-06 Yingzhen Yang , Ping Li

The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…

Optimization and Control · Mathematics 2014-03-20 Florian Bugarin , Adrien Bartoli , Didier Henrion , Jean-Bernard Lasserre , Jean-José Orteu , Thierry Sentenac

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

Optimization and Control · Mathematics 2020-10-06 Francesco Farina , Giuseppe Notarstefano

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

Optimization and Control · Mathematics 2018-12-11 Jianchao Bai , Hongchao Zhang , Jicheng Li

Non-local self-similarity based low rank algorithms are the state-of-the-art methods for image denoising. In this paper, a new method is proposed by solving two issues: how to improve similar patches matching accuracy and build an…

Computer Vision and Pattern Recognition · Computer Science 2020-11-23 Jing Guo , Shuping Wang , Chen Luo , Qiyu Jin , Michael Kwok-Po Ng

In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…

Computational Complexity · Computer Science 2008-12-18 Stephane Zampelli , Martin Mann , Yves Deville , Rolf Backofen

A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…

Discrete Mathematics · Computer Science 2019-10-04 Barış Evrim Demiröz , Kuban Altınel , Lale Akarun

This paper designs a technique route to generate high-quality panoramic image with depth information, which involves two critical research hotspots: fusion of LiDAR and image data and image stitching. For the fusion of 3D points and image…

Computer Vision and Pattern Recognition · Computer Science 2020-10-28 Hao Ma , Jingbin Liu , Zhirong Hu , Hongyu Qiu , Dong Xu , Zemin Wang , Xiaodong Gong , Sheng Yang

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Optimization and Control · Mathematics 2024-04-08 Zhichun Yang , Fu-quan Xia , Kai Tu , Man-Chung Yue

Image-based localization, or camera relocalization, is a fundamental problem in computer vision and robotics, and it refers to estimating camera pose from an image. Recent state-of-the-art approaches use learning based methods, such as…

Computer Vision and Pattern Recognition · Computer Science 2018-06-26 Xiaotian Li , Juha Ylioinas , Juho Kannala

This work proposes a multi-image matching method to estimate semantic correspondences across multiple images. In contrast to the previous methods that optimize all pairwise correspondences, the proposed method identifies and matches only a…

Computer Vision and Pattern Recognition · Computer Science 2018-05-02 Qianqian Wang , Xiaowei Zhou , Kostas Daniilidis

Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Gregory Vaksman , Michael Zibulevsky , Michael Elad