Related papers: Iterative TV minimization on the graph
In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…
This paper is concerned with the numerical minimization of energy functionals in $BV(\Omega)$ (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by…
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal…
We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a…
Bregman iterations are known to yield excellent results for denoising, deblurring and compressed sensing tasks, but so far this technique has rarely been used for other image processing problems. In this paper we give a thorough description…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…
We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based on two distinct sub-networks, with the first sub-network…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical…
Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…
We present a unified approach to compute the total vertex irregularity strength (tvs) of various graphs, employing a novel technique recently proposed by Barra et al. For graphs such as cycles, paths, prisms, wheels, complete graphs, helm…
We introduce Back to Basics (BTB), a fast iterative algorithm for noise reduction. Our method is computationally efficient, does not require training or ground truth data, and can be applied in the presence of independent noise, as well as…
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV)…
We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a variational approach with an infimal convolution of…
A Bayesian factor graph reduced to normal form consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived…
Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical…
We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional…
A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph $G$ and weight function $w: V(G) \to \mathbb{Q}_{\geq 0}$, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set…