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Two-dimensional singular decomposition (2DSVD) has been widely used for image processing tasks, such as image reconstruction, classification, and clustering. However, traditional 2DSVD algorithm is based on the mean square error (MSE) loss,…

Computer Vision and Pattern Recognition · Computer Science 2020-07-07 Miaohua Zhang , Yongsheng Gao

We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation…

Computer Vision and Pattern Recognition · Computer Science 2020-02-13 Jan Lellmann , Dirk A. Lorenz , Carola Schönlieb , Tuomo Valkonen

The aim of this paper is to test and analyze a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our…

Numerical Analysis · Mathematics 2014-07-24 Martin Burger , Jahn Müller , Evangelos Papoutsellis , Carola-Bibiane Schönlieb

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…

Computer Vision and Pattern Recognition · Computer Science 2023-03-09 Yusuke Mukuta , Tatsuya Harada

We propose a new superresolution imaging technique for interferometry using sparse modeling, utilizing two regularization terms: the $\ell_1$-norm and a new function named Total Squared Variation (TSV) of the brightness distribution. TSV is…

Instrumentation and Methods for Astrophysics · Physics 2018-06-06 Kazuki Kuramochi , Kazunori Akiyama , Shiro Ikeda , Fumie Tazaki , Vincent L. Fish , Hung-Yi Pu , Keiichi Asada , Mareki Honma

The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…

Optimization and Control · Mathematics 2015-07-21 Boris S. Mordukhovich , M. Ebrahim Sarabi

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel, we propose to fuse this available data (represented…

Optimization and Control · Mathematics 2021-08-04 Evelyn Cueva , Alexander Meaney , Samuli Siltanen , Matthias J. Ehrhardt

Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D…

Computational Geometry · Computer Science 2016-04-28 Martin Brooks

Recently variational models with priors involving first and second order derivatives resp. differences were successfully applied for image restoration. There are several ways to incorporate the derivatives of first and second order into the…

Numerical Analysis · Mathematics 2018-12-10 Ronny Bergmann , Jan Henrik Fitschen , Johannes Persch , Gabriele Steidl

This paper addresses the solution of inverse problems in imaging given an additional reference image. We combine a modification of the discrete geodesic path model for image metamorphosis with a variational model,actually the $L^2$-$TV$…

Numerical Analysis · Mathematics 2019-05-22 Sebastian Neumayer , Johannes Persch , Gabriele Steidl

In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…

Methodology · Statistics 2020-01-15 Ying Liu , Bowei Yan , Kathleen Merikangas , Haochang Shou

In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field…

Computer Vision and Pattern Recognition · Computer Science 2018-10-31 Jiaming Liu , Yu Sun , Xiaojian Xu , Ulugbek S. Kamilov

We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable…

Numerical Analysis · Mathematics 2022-02-28 P. F. Antonietti , E. Manuzzi

Graph neural networks (GNN) has been demonstrated to be effective in classifying graph structures. To further improve the graph representation learning ability, hierarchical GNN has been explored. It leverages the differentiable pooling to…

Social and Information Networks · Computer Science 2019-12-19 Kaixiong Zhou , Qingquan Song , Xiao Huang , Daochen Zha , Na Zou , Xia Hu

In Part 1, we developed a new technique based on Lipschitz pushforwards for proving the jump set containment property $\mathcal{H}^{m-1}(J_u \setminus J_f)=0$ of solutions $u$ to total variation denoising. We demonstrated that the technique…

Functional Analysis · Mathematics 2020-02-13 Tuomo Valkonen

In this paper, we present the definition of generalized tensor function according to the tensor singular value decomposition (T-SVD) via the tensor T-product. Also, we introduce the compact singular value decomposition (T-CSVD) of tensors…

Numerical Analysis · Mathematics 2019-10-17 Yun Miao , Liqun Qi , Yimin Wei

Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…

Image and Video Processing · Electrical Eng. & Systems 2023-07-19 Diego Valsesia , Giulia Fracastoro , Enrico Magli

This short note is a supplement to [1], in which the total variation of graph distributional signals is introduced and studied. We introduce a different formulation of total variation and relate it to the notion of edge centrality. The…

Signal Processing · Electrical Eng. & Systems 2024-11-04 Feng Ji

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

Numerical Analysis · Mathematics 2024-08-07 Xuan Liu , Zhigang Jia , Xiaoqing Jin

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

Computer Vision and Pattern Recognition · Computer Science 2019-03-22 Jinshi Yu , Chao Li , Qibin Zhao , Guoxu Zhou