17 papers · ranked by Valyu relevance
Zhao‐Rong Lai, Weiwen Wang
Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical essence of IRM remains to be properly explained. We verify that IRM is essentially a…
Huanyu Xu, Quansen Sun, Nan Luo, Guo Cao + 2 more
In this paper, a Bregman iteration based total variation image restoration algorithm is proposed. Based on the Bregman iteration, the algorithm splits the original total variation problem into sub-problems that are easy to solve. Moreover, non-local regularization is introduced into the proposed algorithm, and a method…
Hou-biao Li, Jun-yan Wang, Hong-xia Dou
Restoring Poissonian noise images have drawn a lot of attention in recent years. There are many regularization methods to solve this problem and one of the most famous methods is the total variation model. In this paper, by adding a quadratic regularization on TGV regularization part, a new image restoration model is…
Marko Järvenpää, Robert Piché
A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the 'regularisation parameter', are estimated simultaneously from the data in the model. The model is based on the characterisation of the Laplace density prior as a scale…
Tomoyuki Obuchi, Shiro Ikeda, Kazunori Akiyama, Yoshiyuki Kabashima + 1 more
'Yuanquan Wang'] We develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by ℓ1-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to…
Kui Liu, Jieqing Tan, Liefu Ai
To eliminate the staircasing effect for total variation filter and synchronously avoid the edges blurring for fourth-order PDE filter, a hybrid regularizers-based adaptive anisotropic diffusion is proposed for image denoising. In the proposed model, the $H^{-1}$-norm is considered as the fidelity term and the…
Weijia Huang, Zhongyi Huang, Wenli Yang, Wei Zhu
In this paper, we propose image restoration models using optimal transport (OT) and total variation regularization. We present theoretical results of the proposed models based on the relations between the dual Lipschitz norm from OT and the G-norm introduced by Yves Meyer. We design a numerical method based on the…
Mushtaq Ahmad Khan, Wen Chen, Asmat Ullah, Lin Ji + 1 more
Minimization functionals related to Euler’s elastica energy has a broad range of applications in computer vision and image processing. This paper proposes a novel Euler’s elastica and curvature-based variational model for image restoration corrupted with multiplicative noise. It combines Euler’s elastica curvature with…
Carola‐Bibiane Schönlieb, Zakhar Shumaylov
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging (MRI, CT), remote sensing (Radar), and material sciences (electron microscopy). These problems serve as critical tools for visualizing…
Marianthi Markatou, Yang Chen
One natural way to measure model adequacy is by using statistical distances as loss functions. A related fundamental question is how to construct loss functions that are scientifically and statistically meaningful. In this paper, we investigate non-quadratic distances and their role in assessing the adequacy of a model…
Yan Zhang, Jiasong Wu, Youyong Kong, Gouenou Coatrieux + 2 more
'Huazhong Shu' 'Pew-Thian Yap'] Total variation (TV) based models are very popular in image denoising but suffer from some drawbacks. For example, local TV methods often cannot preserve edges and textures well when they face excessive smoothing. Non-local TV methods constitute an alternative, but their computational…
Marlon E. Cobos, Luis Osorio-Olvera, A. Townsend Peterson
Ecological niche models are popular tools used in fields such as ecology, biogeography, conservation biology, and epidemiology. These models are used commonly to produce representations of species’ potential distributions, which are then used to answer other research questions; for instance, where species richness is…
David M. Blei, Alp Kucukelbir, Jon McAuliffe
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this paper, we review variational inference…
Yudong Qiu, Paul S. Nerenberg, Teresa Head-Gordon, Lee-Ping Wang
In this work we investigate whether experimental surface tension measurements, which are less sensitive to quantum and self-polarization corrections, are able to replace the usual reliance on the heat of vaporization as experimental reference data for fitting force field models of molecular liquids. To test this…
Mario Schlemmer
The variability in population abundances is of central concern for the quantification of evolutionary patterns and an indispensable tool for ecological analysis. Standard measures of population variability are often biased, insensitive to population crashes, and exhibit other pathological behavior. Here I introduce new…
Calistus N. Ngonghala, Sadie J. Ryan, Blanka Tesla, Leah R. Demakovskys + 4 more
When a formerly rare pathogen emerges to cause a pandemic, it is critical to understand the ecology of the disease dynamics and its potential effects on disease control. Here, we take advantage of newly available experimental data to parameterize a temperature-dependent dynamical model of Zika virus (ZIKV)…
Jérôme Darbon, Gabriel P. Langlois, Tingwei Meng
Many imaging problems can be formulated as inverse problems expressed as finite-dimensional optimization problems. These optimization problems generally consist of minimizing the sum of a data fidelity and regularization terms. In [23, 26], connections between these optimization problems and (multi-time)…