4 papers · 1 filter
Real order total variation with applications to the loss functions in learning schemes
Pan Liu, Xin Yang Lu, Kunlun He
Loss function are an essential part in modern data-driven approach, such as bi-level training scheme and machine learnings. In this paper we propose a loss function consisting of a…
Average-distance problem with curvature penalization for data parameterization: regularity of minimizers
Xinyang Lu, Dejan Slepcev
We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functio…
An Asymptotically Compatible Approach For Neumann-Type Boundary Condition On Nonlocal Problems
Huaiqian You, Xin Yang Lu, Nathaniel Trask +1
In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter characterizing the range of nonlocal interactions, and consider the treatment of…
Real order (an)-isotropic total variation in image processing - Part I: analytical analysis and functional properties
Pan Liu, Xin Yang Lu
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the -order (an)-isotropic total variatio…