相关论文: Real order total variation with applications to th…

In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…

This article is the second work in our series of papers dedicated to image processing models based on the fractional order total variation $TV^r$. In our first work of this series, we studied key analytic properties of these semi-norms.…

A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…

New fractional $r$-order seminorms, $TGV^r$, $r\in \mathbb R$, $r\geq 1$, are proposed in the one-dimensional (1D) setting, as a generalization of the integer order $TGV^k$-seminorms, $k\in\mathbb{N}$. The fractional $r$-order…

The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…

We derive a new pointwise characterization of the subdifferential of the total variation (TV) functional. It involves a full trace operator which maps certain $ L^q $ - vectorfields to integrable functions with respect to the total…

In this paper, we introduce the Hessian-Schatten total variation (HTV) -- a novel seminorm that quantifies the total "rugosity" of multivariate functions. Our motivation for defining HTV is to assess the complexity of supervised-learning…

We introduce a novel unsupervised loss function for learning semantic segmentation with deep convolutional neural nets (ConvNet) when densely labeled training images are not available. More specifically, the proposed loss function penalizes…

This paper illustrates the central role of loss functions in data-driven decision making, providing a comprehensive survey on their influence in cost-sensitive classification (CSC) and reinforcement learning (RL). We demonstrate how…

In this paper, we obtain the functional derivatives of a finite horizon error norm between a full-order and a reduced-order continuous-time linear time-varying (LTV) system. Based on the functional derivatives, first-order necessary…

In neural networks, the loss function represents the core of the learning process that leads the optimizer to an approximation of the optimal convergence error. Convolutional neural networks (CNN) use the loss function as a supervisory…

The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…

Ordinal regression is commonly formulated as a multi-class problem with ordinal constraints. The challenge of designing accurate classifiers for ordinal regression generally increases with the number of classes involved, due to the large…

This paper introduces a novel approach to securing machine learning model deployments against potential distribution shifts in practical applications, the Total Variation Out-of-Distribution (TV-OOD) detection method. Existing methods have…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

Temporal difference learning and Residual Gradient methods are the most widely used temporal difference based learning algorithms; however, it has been shown that none of their objective functions is optimal w.r.t approximating the true…

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a…

Loss functions are one of the crucial ingredients in deep learning-based medical image segmentation methods. Many loss functions have been proposed in existing literature, but are studied separately or only investigated with few other…

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…

A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…