Related papers: Iterative TV minimization on the graph
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
An optical flow variational model is proposed for a sequence of images defined on a domain in $\mathbb{R}^2$. We introduce a regularization term given by the $L^1$ norm of a fractional differential operator. To solve the minimization…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector…
This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the…
The $\ell^1$ and total variation (TV) penalties have been used successfully in many areas, and the combination of the $\ell^1$ and TV penalties can lead to further improved performance. In this work, we investigate the mathematical theory…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel,…
To reduce the x-ray dose in computerized tomography (CT), many constrained optimization approaches have been proposed aiming at minimizing a regularizing function that measures lack of consistency with some prior knowledge about the object…
Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a…
The quadratic penalty alternating minimization (AM) method is widely used for solving the convex $\ell_1$ total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0 < p < 1$…
Motivated in part by models arising from mathematical descriptions of Bose-Einstein condensation, we consider total variation minimization problems in which the total variation is weighted by a function that may degenerate near the domain…
A noise-corrupted image often requires interpolation. Given a linear denoiser and a linear interpolator, when should the operations be independently executed in separate steps, and when should they be combined and jointly optimized? We…
We describe an approach for segmenting an image into regions that correspond to surfaces in the scene that are partially surrounded by the medium. It integrates both appearance and motion statistics into a cost functional, that is seeded…
We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to…
In this paper we introduce a novel notion of separation surfaces for image decomposition. A surface is embedded in the spectral total-variation (TV) three dimensional domain and encodes a spatially-varying separation scale. The method…
There are many applications of graph cuts in computer vision, e.g. segmentation. We present a novel method to reformulate the NP-hard, k-way graph partitioning problem as an approximate minimal s-t graph cut problem, for which a globally…