Related papers: Approximation Theory of Total Variation Minimizati…
Inference and learning for probabilistic generative networks is often very challenging and typically prevents scalability to as large networks as used for deep discriminative approaches. To obtain efficiently trainable, large-scale and well…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations.…
While Total Variation (TV) excels in noise reduction and edge preservation, its reliance on a scalar regularization parameter limits adaptivity. In this study, we present a Learnable Total Variation (LTV) framework coupling an unrolled TV…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and other artifacts. Total variation regularization has been…
This paper provides a new algorithm for solving inverse problems, based on the minimization of the $L^2$ norm and on the control of the Total Variation. It consists in relaxing the role of the Total Variation in the classical Total…
Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…
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…
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to…
Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to…
The total variation filtering technique emerges as a highly effective strategy for restoring signals with discontinuities in various parts of their structure. This study presents and implements a one-dimensional signal filtering algorithm…
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…
We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV…
We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide…
This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
We introduce semi-supervised data classification algorithms based on total variation (TV), Reproducing Kernel Hilbert Space (RKHS), support vector machine (SVM), Cheeger cut, labeled and unlabeled data points. We design binary and…