相关论文: On a fast bilateral filtering formulation using fu…

Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…

Video interpolation increases the temporal resolution of a video sequence by synthesizing intermediate frames between two consecutive frames. We propose a novel deep-learning-based video interpolation algorithm based on bilateral motion…

In this paper, a method for recursively computing approximate modal paths is developed. A recursive formulation of the modal path can be obtained either by backward or forward dynamic programming. By combining both methods, a ``two-filter''…

Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…

We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…

We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show…

It is well-known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not depend on the size or shape of the filter. These fast algorithms are generally referred to as constant-time or…

We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…

We propose a simple, interpretable framework for solving a wide range of image reconstruction problems such as denoising and deconvolution. Given a corrupted input image, the model synthesizes a spatially varying linear filter which, when…

The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the…

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in two-dimensional Filtered Backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form,…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using a generalization of the Picard parameter that was…

Set reconciliation protocols typically make two critical assumptions: they are designed for fixed-sized elements and they are optimized for when the difference cardinality, d, is very small. When adapting to variable-sized elements, the…

Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of…

There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…

This paper deals with the design of discrete-time algorithms for the robust filtering differentiator. Two discrete-time realizations of the filtering differentiator are introduced. The first one, which is based on an exact discretization of…

This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow…

By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…