An introduction to continuous optimization for imaging

A Chambolle, T Pock - Acta Numerica, 2016 - cambridge.org
A large number of imaging problems reduce to the optimization of a cost function, with
typical structural properties. The aim of this paper is to describe the state of the art in …

Higher-order total variation approaches and generalisations

K Bredies, M Holler - Inverse Problems, 2020 - iopscience.iop.org
Over the last decades, the total variation (TV) has evolved to be one of the most broadly-
used regularisation functionals for inverse problems, in particular for imaging applications …

An introduction to total variation for image analysis

A Chambolle, V Caselles, D Cremers… - … numerical methods for …, 2010 - degruyter.com
These notes address various theoretical and practical topics related to Total Variationbased
image reconstruction. They focus first on some theoretical results on functions which …

[图书][B] Image processing and analysis: variational, PDE, wavelet, and stochastic methods

TF Chan, J Shen - 2005 - SIAM
No time in human history has ever witnessed such explosive influence and impact of image
processing on modern society, sciences, and technologies. From nanotechnologies …

An algorithm for minimizing the Mumford-Shah functional

T Pock, D Cremers, H Bischof… - 2009 IEEE 12th …, 2009 - ieeexplore.ieee.org
In this work we revisit the Mumford-Shah functional, one of the most studied variational
approaches to image segmentation. The contribution of this paper is to propose an algorithm …

Total variation minimization and a class of binary MRF models

A Chambolle - … Workshop on Energy Minimization Methods in …, 2005 - Springer
We observe that there is a strong connection between a whole class of simple binary MRF
energies and the Rudin-Osher-Fatemi (ROF) Total Variation minimization approach to …

A convex relaxation approach for computing minimal partitions

T Pock, A Chambolle, D Cremers… - 2009 IEEE conference …, 2009 - ieeexplore.ieee.org
In this work we propose a convex relaxation approach for computing minimal partitions. Our
approach is based on rewriting the minimal partition problem (also known as Potts model) in …

A convex approach to minimal partitions

A Chambolle, D Cremers, T Pock - SIAM Journal on Imaging Sciences, 2012 - SIAM
We describe a convex relaxation for a family of problems of minimal perimeter partitions. The
minimization of the relaxed problem can be tackled numerically: we describe an algorithm …

Global solutions of variational models with convex regularization

T Pock, D Cremers, H Bischof, A Chambolle - SIAM Journal on Imaging …, 2010 - SIAM
We propose an algorithmic framework for computing global solutions of variational models
with convex regularity terms that permit quite arbitrary data terms. While the minimization of …

Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty

K Bredies - Efficient Algorithms for Global Optimization Methods in …, 2014 - Springer
We study and extend the recently introduced total generalized variation (TGV) functional for
multichannel images. This functional has already been established to constitute a well …