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In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

Optimization and Control · Mathematics 2022-08-31 Zhenyuan Zhu , Fan Chen , Junyu Zhang , Zaiwen Wen

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…

Optimization and Control · Mathematics 2021-11-16 Bin Gao , Xin Liu , Ya-xiang Yuan

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

Numerical Analysis · Mathematics 2025-06-24 Chai Wah Wu , Mark S. Squillante , Vasileios Kalantzis , Lior Horesh

Malicious image manipulation poses societal risks, increasing the importance of effective image manipulation detection methods. Recent approaches in image manipulation detection have largely been driven by fully supervised approaches, which…

Computer Vision and Pattern Recognition · Computer Science 2025-04-01 Xinghao Wang , Tao Gong , Qi Chu , Bin Liu , Nenghai Yu

Single image super-resolution (SISR) aims to obtain a high-resolution output from one low-resolution image. Currently, deep learning-based SISR approaches have been widely discussed in medical image processing, because of their potential to…

Image and Video Processing · Electrical Eng. & Systems 2021-05-25 Jin Zhu , Chuan Tan , Junwei Yang , Guang Yang , Pietro Lio'

Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…

Machine Learning · Statistics 2024-05-28 Xunpeng Huang , Difan Zou , Yi-An Ma , Hanze Dong , Tong Zhang

Sharpness-Aware Minimization (SAM) has emerged as a promising approach for effectively reducing the generalization error. However, SAM incurs twice the computational cost compared to base optimizer (e.g., SGD). We propose Asymptotic…

Computer Vision and Pattern Recognition · Computer Science 2025-03-31 Jiaxin Deng , Junbiao Pang , Baochang Zhang

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a…

Signal Processing · Electrical Eng. & Systems 2022-02-28 Alexander Lin , Andrew H. Song , Berkin Bilgic , Demba Ba

Anomaly detection remains an open challenge in many application areas. While there are a number of available machine learning algorithms for detecting anomalies, analysts are frequently asked to take additional steps in reasoning about the…

Human-Computer Interaction · Computer Science 2022-05-24 Brian Montambault , Camelia D. Brumar , Michael Behrisch , Remco Chang

Insufficient prior knowledge of a captured hyperspectral image (HSI) scene may lead the experts or the automatic labeling systems to offer incorrect labels or ambiguous labels (i.e., assigning each training sample to a group of candidate…

Computer Vision and Pattern Recognition · Computer Science 2024-05-28 Shujun Yang , Yu Zhang , Yao Ding , Danfeng Hong

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

Machine Learning · Computer Science 2010-11-17 Curzio Basso , Matteo Santoro , Alessandro Verri , Silvia Villa

Synthesizing high quality saliency maps from noisy images is a challenging problem in computer vision and has many practical applications. Samples generated by existing techniques for saliency detection cannot handle the noise perturbations…

Computer Vision and Pattern Recognition · Computer Science 2019-04-03 Prerana Mukherjee , Manoj Sharma , Megh Makwana , Ajay Pratap Singh , Avinash Upadhyay , Akkshita Trivedi , Brejesh Lall , Santanu Chaudhury

Stochastic Approximation (SA) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with…

Optimization and Control · Mathematics 2023-07-18 Aymeric Dieuleveut , Gersende Fort , Eric Moulines , Hoi-To Wai

The hard margin loss function has been at the core of the support vector machine (SVM) research from the very beginning due to its generalization capability.On the other hand, the cardinality constraint has been widely used for feature…

Optimization and Control · Mathematics 2023-08-01 Penghe Zhang , Naihua Xiu , Hou-Duo Qi

The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…

Numerical Analysis · Mathematics 2022-03-30 Yanjun Zhang , Hanyu Li

A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…

Machine Learning · Computer Science 2018-08-23 Katsuyuki Hagiwara

Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…

Optimization and Control · Mathematics 2019-01-28 Fabian Pedregosa , Kilian Fatras , Mattia Casotto

Hyperspectral image (HI) analysis approaches have recently become increasingly complex and sophisticated. Recently, the combination of spectral-spatial information and superpixel techniques have addressed some hyperspectral data issues,…

Image and Video Processing · Electrical Eng. & Systems 2024-07-23 Luciano Carvalho Ayres , Sérgio José Melo de Almeida , José Carlos Moreira Bermudez , Ricardo Augusto Borsoi

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

Optimization and Control · Mathematics 2016-11-15 Manya V. Afonso , Jose M. Bioucas-Dias , Mario A. T. Figueiredo

Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we…

Robotics · Computer Science 2024-10-28 Barbara Bazzana , Henrik Andreasson , Giorgio Grisetti