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This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…

Numerical Analysis · Mathematics 2025-09-01 Mohamed El Guide , Anas El Hachimi , Khalide Jbilou , Lothar Reichel

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

Machine Learning · Statistics 2016-10-18 Lingxiao Wang , Xiao Zhang , Quanquan Gu

Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm…

Computer Vision and Pattern Recognition · Computer Science 2016-11-03 Yuan Xie , Shuhang Gu , Yan Liu , Wangmeng Zuo , Wensheng Zhang , Lei Zhang

Traditional range-instantaneous Doppler (RID) methods for rigid-body target imaging often suffer from low resolution due to the limitations of time-frequency analysis (TFA). To address this challenge, our primary focus is on obtaining high…

Computer Vision and Pattern Recognition · Computer Science 2025-03-31 Boan Zhang , Hang Dong , Jiongge Zhang , Long Tian , Rongrong Wang , Zhenhua Wu , Xiyang Liu , Hongwei Liu

A common strategy in variational image recovery is utilizing the nonlocal self-similarity (NSS) property, when designing energy functionals. One such contribution is nonlocal structure tensor total variation (NLSTV), which lies at the core…

Image and Video Processing · Electrical Eng. & Systems 2024-11-12 Ezgi Demircan-Tureyen , Mustafa E. Kamasak

This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…

Optimization and Control · Mathematics 2017-03-22 Carl Olsson , Marcus Carlsson , Fredrik Andersson , Viktor Larsson

Deep learning models in satellite onboard enable real-time interpretation of remote sensing images, reducing the need for data transmission to the ground and conserving communication resources. As satellite numbers and observation…

Computer Vision and Pattern Recognition · Computer Science 2024-06-05 Xinyang Pu , Feng Xu

In this work, we propose norm-bounded low-rank adaptation (NB-LoRA) for parameter-efficient fine tuning. NB-LoRA is a novel parameterization of low-rank weight adaptations that admits explicit bounds on each singular value of the adaptation…

Machine Learning · Computer Science 2025-09-30 Ruigang Wang , Krishnamurthy Dvijotham , Ian R. Manchester

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

Machine Learning · Statistics 2021-09-28 April Sagan , John E. Mitchell

We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set…

Optimization and Control · Mathematics 2017-04-13 Ankit Parekh , Ivan W. Selesnick

Despite the impressive representation capacity of vision transformer models, current light-weight vision transformer models still suffer from inconsistent and incorrect dense predictions at local regions. We suspect that the power of their…

Computer Vision and Pattern Recognition · Computer Science 2021-12-22 Chenglin Yang , Yilin Wang , Jianming Zhang , He Zhang , Zijun Wei , Zhe Lin , Alan Yuille

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…

Numerical Analysis · Mathematics 2025-01-20 Elena Morotti , Davide Evangelista , Andrea Sebastiani , Elena Loli Piccolomini

Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often…

Machine Learning · Statistics 2026-05-08 Chengyu Cui , Gongjun Xu

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Computer Vision and Pattern Recognition · Computer Science 2020-03-13 Pawan Goyal , Hussam Al Daas , Peter Benner

In image denoising (IDN) processing, the low-rank property is usually considered as an important image prior. As a convex relaxation approximation of low rank, nuclear norm based algorithms and their variants have attracted significant…

Image and Video Processing · Electrical Eng. & Systems 2020-04-03 Yanwei Zhao , Ping Yang , Qiu Guan , Jianwei Zheng , Wanliang Wang

Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization…

Computer Vision and Pattern Recognition · Computer Science 2017-11-22 Qiong Wang , Xinggan Zhang , Yu Wu , Lan Tang , Zhiyuan Zha

Small moving target detection is crucial for many defense applications but remains highly challenging due to low signal-to-noise ratios, ambiguous visual cues, and cluttered backgrounds. In this work, we propose a novel deep learning…

Computer Vision and Pattern Recognition · Computer Science 2025-09-10 Guoyi Zhang , Siyang Chen , Guangsheng Xu , Zhihua Shen , Han Wang , Xiaohu Zhang

Tensor robust principal component analysis (TRPCA) is a classical way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular value equally. However, for real-world visual data,…

Computer Vision and Pattern Recognition · Computer Science 2023-07-10 Xiaoyu Geng , Qiang Guo , Shuaixiong Hui , Ming Yang , Caiming Zhang

Non-Local Attention (NLA) brings significant improvement for Single Image Super-Resolution (SISR) by leveraging intrinsic feature correlation in natural images. However, NLA gives noisy information large weights and consumes quadratic…

Computer Vision and Pattern Recognition · Computer Science 2022-03-11 Bin Xia , Yucheng Hang , Yapeng Tian , Wenming Yang , Qingmin Liao , Jie Zhou

Detecting tiny objects is one of the main obstacles hindering the development of object detection. The performance of generic object detectors tends to drastically deteriorate on tiny object detection tasks. In this paper, we point out that…

Computer Vision and Pattern Recognition · Computer Science 2022-10-18 Chang Xu , Jinwang Wang , Wen Yang , Huai Yu , Lei Yu , Gui-Song Xia
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