A study of the one dimensional total generalised variation regularisation problem

DOI10.3934/ipi.2015.9.511zbMath1336.49044arXiv1309.5900OpenAlexW2963042087WikidataQ57561956 ScholiaQ57561956MaRDI QIDQ256021

Kristian Bredies, Konstantinos Papafitsoros

Publication date: 9 March 2016

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.5900

zbMATH Keywords

inverse problemsstaircasingimage denoisinghigher order regularizationtotal generalized variation

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Inverse problems in optimal control (49N45) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (18)

Analytical aspects of spatially adapted total variation regularisation ⋮ Infimal convolution regularisation functionals of BV and \(\mathrm{L}^p\) spaces. I: The finite \(p\) case ⋮ The jump set under geometric regularisation. II: Higher-order approaches ⋮ Flows generating nonlinear eigenfunctions ⋮ Analysis and Application of a Nonlocal Hessian ⋮ Nonlinear spectral analysis via one-homogeneous functionals: overview and future prospects ⋮ Signal recovery via TV-type energies ⋮ An alternative approach towards the higher order denoising of images. analytical aspects ⋮ Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization ⋮ Asymptotic Behaviour of Total Generalised Variation ⋮ Inverse scale space decomposition ⋮ Unnamed Item ⋮ Exact solutions for the total variation denoising problem of piecewise constant images in dimension one ⋮ A denoising model adapted for impulse and Gaussian noises using a constrained-PDE ⋮ Analysis and automatic parameter selection of a variational model for mixed Gaussian and salt-and-pepper noise removal ⋮ On the taut string interpretation and other properties of the Rudin-Osher-Fatemi model in one dimension ⋮ The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising ⋮ Multiscale Segmentation via Bregman Distances and Nonlinear Spectral Analysis

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