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—We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals(More)
This paper proposes a new method for image compression. The method is based on the approximation of an image, regarded as a function , by a linear spline over an adapted triangulation, D(Y), which is the Delaunay triangulation of a small set Y of significant pixels. The linear spline minimizes the distance to the image, measured by the mean square error,(More)
— Locally optimal Delaunay triangulations are constructed to improve previous image approximation schemes. Our construction relies on a local optimization procedure, termed exchange. The efficient implementation of the exchange algorithm is addressed and its complexity is discussed. The good performance of our improved image approximation is illustrated by(More)
Adaptive thinning algorithms are greedy point removal schemes for bivariate scattered data sets with corresponding function values, where the points are recursively removed according to some data-dependent criterion. Each subset of points, together with its function values, defines a linear spline over its Delaunay triangulation. The basic criterion for the(More)
Many algorithms in image processing rely on the computation of sums of pixel values over a large variety of subsets of the image domain. This includes the computation of image moments for pattern recognition purposes, or adaptive smoothing and regression methods, such as wedgelets. In the first part of the paper, we present a general method which allows the(More)
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 p-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.(More)
In this paper a new very low bit rate scalable encoding principle is presented. It is based on hierarchical triangular mesh encoding combined with triangle based DCT coding. Affine or DCT approximation is selected according to best rate distorsion trade-off. In this way our coder demonstrates advantages at very low bit rates avoiding the traditional block(More)
We investigate the nonsmooth and nonconvex L 1-Potts functional in discrete and continuous time. We show Γ-convergence of discrete L 1-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretiza-tion gets finer. For the discrete L 1-Potts problem, we introduce an O(n 2) time and(More)
We propose a new analysis tool for signals that is based on complex wavelet signs, called a signature. The complex-valued signature of a signal at some spatial location is defined as the fine-scale limit of the signs of its complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient(More)
We present a mathematical model and computer simulations for the control of a pathogenic biofilm by a probiotic biofilm. This is a substantial extension of a previous model of control of a pathogenic biofilm by microbial control agents that are suspended in the aqueous bulk phase (H. Khassehkhan and H.J. Eberl, Comp. Math. Meth. Med, 9(1) (2008), pp.(More)