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Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…

We investigate the problem of agent-to-agent interaction in decentralized (federated) learning over time-varying directed graphs, and, in doing so, propose a consensus-based algorithm called DSGTm-TV. The proposed algorithm incorporates…

Unsupervised disentanglement of static appearance and dynamic motion in video remains a fundamental challenge, often hindered by information leakage and blurry reconstructions in existing VAE- and GAN-based approaches. We introduce DiViD,…

For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically…

Direction-guided structure tensor total variation (DSTV) is a recently proposed regularization term that aims at increasing the sensitivity of the structure tensor total variation (STV) to the changes towards a predetermined direction.…

Gradient-based methods successfully train highly overparameterized models in practice, even though the associated optimization problems are markedly nonconvex. Understanding the mechanisms that make such methods effective has become a…

Deep learning has achieved tremendous success by training increasingly large models, which are then compressed for practical deployment. We propose a drastically different approach to compact and optimal deep learning: We decouple the…

Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a…

We introduce test prediction variance (TPV)--the first-order sensitivity of a trained model's outputs to parameter perturbations--as a unifying framework for analyzing post-training robustness. TPV is a fully label-free object whose trace…

In this work, we propose a new discretization for second-order total generalized variation (TGV) with some distinct properties compared to existing discrete formulations. The introduced model is based on same design principles as Condat's…

Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…

Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine…

Computed tomography is widely used as an imaging tool to visualize three-dimensional structures with expressive bone-soft tissue contrast. However, CT resolution and radiation dose are tightly entangled, highlighting the importance of…

Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven…

Gridization, the process of partitioning space into grids where users share similar channel characteristics, serves as a fundamental prerequisite for efficient large-scale network optimization. However, existing methods like Geographical or…

Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of…

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

This paper describes a novel algorithmic framework to minimize a finite-sum of functions available over a network of nodes. The proposed framework, that we call~\GTVR, is stochastic and decentralized, and thus is particularly suitable for…

In this work, we study an optimizer, Grad-Avg to optimize error functions. We establish the convergence of the sequence of iterates of Grad-Avg mathematically to a minimizer (under boundedness assumption). We apply Grad-Avg along with some…

Quantization of Convolutional Neural Networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the…