Related papers: Total Variation and Euler's Elastica for Supervise…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
The variational autoencoder (VAE) typically employs a standard normal prior as a regularizer for the probabilistic latent encoder. However, the Gaussian tail often decays too quickly to effectively accommodate the encoded points, failing to…
Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…
Total variation denoising (TVD) is a classical method for denoising and curve fitting, yet an explicit pointwise description of its fitted values has only recently been established in the mean regression setting by arXiv:2410.03041v4. This…
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we propose a Fourier-domain variational formulation for…
Deep metric learning has been demonstrated to be highly effective in learning semantic representation and encoding information that can be used to measure data similarity, by relying on the embedding learned from metric learning. At the…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We address the problem of visual knowledge adaptation by leveraging labeled patterns from source domain and a very limited number of labeled instances in target domain to learn a robust classifier for visual categorization. This paper…
We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…
As one of the most popular generative models, Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. However, when the decoder network is sufficiently expressive, VAE may lead…
In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…
In this paper, we are concerned with a modified Euler scheme for the SDE under consideration, where the drift is of super-linear growth and dissipative merely outside a closed ball. By adopting the synchronous coupling, along with the…
We study the convergence of gradient methods for the training of mean-field single-hidden-layer neural networks with square loss. For this high-dimensional and non-convex optimization problem, most known convergence results are either…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
Self-supervised methods have recently proved to be nearly as effective as supervised ones in various imaging inverse problems, paving the way for learning-based approaches in scientific and medical imaging applications where ground truth…
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…
Classical optimization theory deals with fixed, time-invariant objective functions. However, time-varying optimization has emerged as an important subject for decision-making in dynamic environments. In this work, we study the problem of…
Learning the optimized solution as a function of environmental parameters is effective in solving numerical optimization in real time for time-sensitive applications. Existing works of learning to optimize train deep neural networks (DNN)…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…