Related papers: Total variation regularization with variable Lebes…
The problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques…
Total variation has proved its effectiveness in solving inverse problems for compressive sensing. Besides, the nonlocal means filter used as regularization preserves texture better for recovered images, but it is quite complex to implement.…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that…
We obtain results concerning the so-called factorization for the convergence of random variables almost everywhere (almost surely or with probability one), belonging to the classical Lebesgue-Riesz spaces and we extend these results to the…
The total variation (TV) model and its related variants have already been proposed for image processing in previous literature. In this paper a novel total variation model based on kernel functions is proposed. In this novel model, we first…
Optimization within a layer of a deep-net has emerged as a new direction for deep-net layer design. However, there are two main challenges when applying these layers to computer vision tasks: (a) which optimization problem within a layer is…
Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new…
We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper,…
This paper presents a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a total variation (TV) sparsity prior. Because of the prior used, and the fact that the prior parameters are estimated…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP)…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
In recent works several authors have proposed the use of precise boundary conditions (BCs) for blurring models and they proved that the resulting choice (Neumann or reflective, anti-reflective) leads to fast algorithms both for deblurring…
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…
A homogenization principle for total variation We prove an inequality comparing the variational distance between pairs of product probability measures to its homogenized counterpart. If $P_1,\ldots,P_n,Q_1,\ldots,Q_n$ are arbitrary…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…