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In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image…

Image and Video Processing · Electrical Eng. & Systems 2022-06-15 Yi-Si Luo , Xi-Le Zhao , Tai-Xiang Jiang , Yi Chang , Michael K. Ng , Chao Li

We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…

Optimization and Control · Mathematics 2025-10-24 Matthias J. Ehrhardt , Subhadip Mukherjee , Hok Shing Wong

Recent studies revealed that convolutional neural networks do not generalize well to small image transformations, e.g. rotations by a few degrees or translations of a few pixels. To improve the robustness to such transformations, we propose…

Computer Vision and Pattern Recognition · Computer Science 2022-08-23 Adrian Sandru , Mariana-Iuliana Georgescu , Radu Tudor Ionescu

We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…

Computer Vision and Pattern Recognition · Computer Science 2013-09-19 Gilles Puy , Pierre Vandergheynst

Adaptive image restoration models can restore images with different degradation levels at inference time without the need to retrain the model. We present an approach that is highly accurate and allows a significant reduction in the number…

Computer Vision and Pattern Recognition · Computer Science 2023-02-28 Shai Aharon , Gil Ben-Artzi

When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…

Image and Video Processing · Electrical Eng. & Systems 2020-06-17 Kalliopi Basioti , George V. Moustakides

Most existing methods usually formulate the non-blind deconvolution problem into a maximum-a-posteriori framework and address it by manually designing kinds of regularization terms and data terms of the latent clear images. However,…

Computer Vision and Pattern Recognition · Computer Science 2022-07-21 Pin-Hung Kuo , Jinshan Pan , Shao-Yi Chien , Ming-Hsuan Yang

Scarcity of labeled data has motivated the development of semi-supervised learning methods, which learn from large portions of unlabeled data alongside a few labeled samples. Consistency Regularization between model's predictions under…

Computer Vision and Pattern Recognition · Computer Science 2020-07-16 Aamir Mustafa , Rafal K. Mantiuk

In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…

Optimization and Control · Mathematics 2025-06-16 Guozhi Dong , Michael Hintermüller , Clemens Sirotenko

Due to adverse atmospheric and imaging conditions, natural images suffer from various degradation phenomena. Consequently, image restoration has emerged as a key solution and garnered substantial attention. Although recent Transformer…

Image and Video Processing · Electrical Eng. & Systems 2025-05-12 Xingyu Jiang , Ning Gao , Xiuhui Zhang , Hongkun Dou , Shaowen Fu , Xiaoqing Zhong , Hongjue Li , Yue Deng

Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…

Machine Learning · Computer Science 2021-02-22 Ruyuan Qu , Jiaqi He , Hui Feng , Chongbin Xu , Bo Hu

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

Numerical Analysis · Mathematics 2026-01-21 Aryeh Keating , Mirjeta Pasha

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from…

Optics · Physics 2017-11-16 Chenglong Bao , George Barbastathis , Hui Ji , Zuowei Shen , Zhengyun Zhang

The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according…

Classical Analysis and ODEs · Mathematics 2024-12-20 Dong Cheng , Kit Ian Kou

In image restoration tasks, like denoising and super resolution, continual modulation of restoration levels is of great importance for real-world applications, but has failed most of existing deep learning based image restoration methods.…

Computer Vision and Pattern Recognition · Computer Science 2019-06-04 Jingwen He , Chao Dong , Yu Qiao

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…

Optimization and Control · Mathematics 2020-02-19 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

Brain image registration transforms a pair of images into one system with the matched imaging contents, which is of essential importance for brain image analysis. This paper presents a novel framework for unsupervised 3D brain image…

Computer Vision and Pattern Recognition · Computer Science 2019-07-04 Lihao Liu , Xiaowei Hu , Lei Zhu , Pheng-Ann Heng

We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…

Optimization and Control · Mathematics 2024-03-13 Carlo Santambrogio , Monica Pragliola , Alessandro Lanza , Marco Donatelli , Luca Calatroni

We derive a memory-efficient first-order variable splitting algorithm for convex image reconstruction problems with non-smooth regularization terms. The algorithm is based on a primal-dual approach, where one of the dual variables is…

Optimization and Control · Mathematics 2019-04-02 Greg Ongie , Naveen Murthy , Laura Balzano , Jeffrey A. Fessler

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

Numerical Analysis · Mathematics 2020-01-08 Maurizio Falcone , Giulio Paolucci , Silvia Tozza