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We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…

Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…

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.…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Many applications require an understanding of an image that goes beyond the simple detection and classification of its objects. In particular, a great deal of semantic information is carried in the relationships between objects. We have…

While deep feature learning has revolutionized techniques for static-image understanding, the same does not quite hold for video processing. Architectures and optimization techniques used for video are largely based off those for static…

We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…

The use of latent variable models has shown to be a powerful tool for modeling probability distributions over sequences. In this paper, we introduce a new variational model that extends the recurrent network in two ways for the task of…

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…

We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…

Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…

Image deblurring is a fundamental and challenging low-level vision problem. Previous vision research indicates that edge structure in natural scenes is one of the most important factors to estimate the abilities of human visual perception.…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…

In this paper we describe a new method for detecting and counting a repeating object in an image. While the method relies on a fairly sophisticated deformable part model, unlike existing techniques it estimates the model parameters in an…

We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…

Edges are a basic and fundamental feature in image processing, that are used directly or indirectly in huge amount of applications. Inspired by the expansion of image resolution and processing power dilated convolution techniques appeared.…