Related papers: Iterative TV minimization on the graph
We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…
In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…
Investigation of image reconstruction from data collected over a limited angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
We propose a denoising method for multimodal graph signals by an alternating minimization scheme that sequentially solves signal restoration and graph learning problems. Many complex-structured data, i.e., those on sensor networks, can…
We study codes on graphs combined with an iterative message passing algorithm for quantization. Specifically, we consider the binary erasure quantization (BEQ) problem which is the dual of the binary erasure channel (BEC) coding problem. We…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
In this paper, we consider using total variation minimization to recover signals whose gradients have a sparse support, from a small number of measurements. We establish the proof for the performance guarantee of total variation (TV)…
We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
The problem of image blurring is one of the most studied topics in the field of image processing. Image blurring is caused by various factors such as hand or camera shake. To restore the blurred image, it is necessary to know information…
We consider one-dimensional variants of the classical first order total variation denoising model introduced by Rudin, Osher and Fatemi. This study is based on our previous work on various denoising and inpainting problems in image…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total…
In this paper, we propose a variational approach for video denoising, based on a total directional variation (TDV) regulariser proposed in Parisotto et al. (2018), for image denoising and interpolation. In the TDV regulariser, the…
This paper develops an algorithm that identifies and decomposes a median graph of a triangulation of a 2-dimensional (2D) oriented bordered surface and in addition restores all corresponding triangulation whenever they exist. The algorithm…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…