We construct a family of trees on which a lazy simple random walk exhibits total variation cutoff. The main idea behind the construction is that hitting times of large sets should be concentrated around their means. For this sequence of trees we compute the mixing time, the relaxation time and the cutoff window.

Total Variation (TV) regularization is a powerful technique for image reconstruction tasks such as denoising, in-painting, and deblurring, because of its ability to produce sharp edges in the images. In this talk we discuss the use of TV regularization for tomographic imaging, where we compute a 2D or 3D reconstruction from noisy projections. We demonstrate that for a small signal-to-noise rati...

We consider solution-driven adaptive variants of Total Variation, in which the adaptivity is introduced as a fixed point problem. We provide existence theory for such fixed points in the continuous domain. For the applications of image denoising, deblurring and inpainting, we provide experiments which demonstrate that our approach in most cases outperforms state-of-the-art regularization approa...

We introduce a novel second-order regularizer, the Affine Total-Variation term, to capture the geometry of piecewise affine functions. The approach is characterized by two convex decompositions of a given image into piecewise affine structure and texture and noise, respectively. A convergent multiplier-based method is presented for computing a global optimum by computationally cheap iterative s...

The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We prove that under general hypotheses the method of lines in well posed in l ∩ BV and we give precise sufficient conditions to establish that the total variat...

We propose a variational model for artifact-free JPEG decompression. It bases on the minimization of the total variation (TV) over the convex set U of all possible source images associated with given JPEG data. The general case where U represents a pointwise restriction with respect to a Lorthonormal basis is considered. Analysis of the infinite dimensional model is presented, including the der...

Total Variation (TV) methods, introduced by L. Rudin and S. Osher a few years ago, are very e ective for the recovery of blocky, possibly discontinuous images, from noisy data. Unfortunately they are not so e ective for the recovery of textured regions. To improve this, recently, L. Rudin introduced a novel functional, the Multiscale Total Variation (MTV). The functional is designed so that it ...

The widely used Total Variation de-noising algorithm can preserve sharp edge, while removing noise. However, since fixed regularization parameter over entire image, small details and textures are often lost in the process. In this paper, we propose a modified Total Variation algorithm to better preserve smaller-scaled features. This is done by allowing an adaptive regularization parameter to co...

We propose and analyze an algorithm for the solution of the L2-subgradient flow of the total variation functional. The algorithm involves no regularization, thus the numerical solution preserves the main features that motivate practitioners to consider this type of energy. We propose an iterative scheme for the solution of the arising problems, show that the iterations converge, and develop a s...

Constrained total variation minimization and related convex optimization problems have applications in many areas of image processing and computer vision such as image reconstruction, enhancement, noise removal, and segmentation. We propose a new method to approximately solve this problem. Numerical experiments show that this method gets close to the globally optimal solution, and is 15-100 tim...