This paper considers the use of the anisotropic total variation seminorm to recover a two dimensional vector x ∈ CN×N from its partial Fourier coefficients, sampled along Cartesian lines. We prove that if (xk,j − xk−1,j)k,j has at most s1 nonzero coefficients in each column and (xk,j − xk,j−1)k,j has at most s2 nonzero coefficients in each row, then, up to multiplication by log factors, one can...

We present a novel deconvolution approach to accurately restore piecewise smooth signals from blurred data. The first stage uses Higher Order Total Variation restorations to obtain an estimate of the location of jump discontinuities from the blurred data. In the second stage the estimated jump locations are used to determine the local orders of a Variable Order Total Variation restoration. The ...

We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with -type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoisin...

in this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of tvd (total variation diminishing) of the solution, is proposed. this scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. schemes preserving the essential physical property of tvd are of great importance in practice. such s...