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In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2015-04-29 Chen Chen , Junzhou Huang , Lei He , Hongsheng Li

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…

Optimization and Control · Mathematics 2015-05-14 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

It is broadly known that deep neural networks are susceptible to being fooled by adversarial examples with perturbations imperceptible by humans. Various defenses have been proposed to improve adversarial robustness, among which adversarial…

Machine Learning · Computer Science 2023-03-30 Wei Wei , Jiahuan Zhou , Ying Wu

Neural implicit modeling permits to achieve impressive 3D reconstruction results on small objects, while it exhibits significant limitations in large indoor scenes. In this work, we propose a novel neural implicit modeling method that…

Computer Vision and Pattern Recognition · Computer Science 2023-09-14 Federico Lincetto , Gianluca Agresti , Mattia Rossi , Pietro Zanuttigh

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…

Machine Learning · Computer Science 2018-06-08 Samet Oymak

Coded aperture is a promising approach for capturing the 4-D light field (LF), in which the 4-D data are compressively modulated into 2-D coded measurements that are further decoded by reconstruction algorithms. The bottleneck lies in the…

Image and Video Processing · Electrical Eng. & Systems 2020-07-24 Mantang Guo , Junhui Hou , Jing Jin , Jie Chen , Lap-Pui Chau

In this paper, we introduce a new regularization technique for transfer learning. The aim of the proposed approach is to capture statistical relationships among convolution filters learned from a well-trained network and transfer this…

Computer Vision and Pattern Recognition · Computer Science 2017-08-24 Mehmet Aygün , Yusuf Aytar , Hazım Kemal Ekenel

This paper presents a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a total variation (TV) sparsity prior. Because of the prior used, and the fact that the prior parameters are estimated…

Signal Processing · Electrical Eng. & Systems 2019-05-06 Victor Churchill , Anne Gelb

Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been…

Image and Video Processing · Electrical Eng. & Systems 2021-09-28 Sayantan Bhadra , Varun A. Kelkar , Frank J. Brooks , Mark A. Anastasio

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the…

Optimization and Control · Mathematics 2014-11-11 Audrey Repetti , Mai Quyen Pham , Laurent Duval , Emilie Chouzenoux , Jean-Christophe Pesquet

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

In this paper we extend the state-of-the-art filtered backprojection (FBP) method with application of the concept of Total Variation regularization. We compare the performance of the new algorithm with the most common form of regularizing…

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

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…

Image and Video Processing · Electrical Eng. & Systems 2023-06-14 Congpei An , Hao-Ning Wu , Xiaoming Yuan

Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…

Image and Video Processing · Electrical Eng. & Systems 2025-11-20 Nabiha Choudhury , Jianqing Jia , Yifei Lou

We propose a novel deep neural network architecture by mapping the robust proximal gradient scheme for fast image reconstruction in parallel MRI (pMRI) with regularization function trained from data. The proposed network learns to…

Image and Video Processing · Electrical Eng. & Systems 2020-08-19 Wanyu Bian , Yunmei Chen , Xiaojing Ye

Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…

Optimization and Control · Mathematics 2021-02-09 Yan-ran Li , Raymond H. F. Chan , Lixin Shen , Xiaosheng Zhuang

In continual learning, the primary challenge is to learn new information without forgetting old knowledge. A common solution addresses this trade-off through regularization, penalizing changes to parameters critical for previous tasks. In…

Machine Learning · Computer Science 2026-04-22 Pourya Shamsolmoali , Masoumeh Zareapoor , Eric Granger , William A. P. Smith , Yue Lu

In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…

Numerical Analysis · Mathematics 2022-09-14 Alireza Hosseini