An introduction to continuous optimization for imaging

By Antonin Chambolle, Thomas Pock. Acta Numerica, 2016

566 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/5c14f75967a5af8cc24937ae61b4f84a2270c13e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

A New Primal–Dual Algorithm for Minimizing the Sum of Three Functions with a Linear Operator (2016, background): “The primal–dual algorithms for two and three functions are reviewed by [23] and specially for image processing problems by [5].”
A primal-dual algorithm with optimal stepsizes and its application in decentralized consensus optimization (2017, background): “Minimizing the sum of two functions has applications in a variety of areas including image processing, machine learning, and decentralized consensus optimization [2,3,12,19].”
Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms (2020, background): “Many problems in statistics, machine learning, or signal processing can be formulated as highdimensional convex optimization problems [3,12,56,59,68,69].”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, background): “A very common example is a least-squares penalty, in particular to solve inverse problems [5]; that is, for some bounded linear operator 𝐴 from X to some real Hilbert space Y and some ∈ Y .”
Learning a Variational Network for Reconstruction of Accelerated MRI Data (2017, background): “l=1 √ |Dure|(2)l,1 + |Duim|(2)l,1 + |Dure|(2)l,2 + |Duim|(2)l,2 where D : R 7→ RN×2 is a finite differences approximation of the image gradient, see for example (27).”
Distributed Proximal Splitting Algorithms with Rates and Acceleration (2020, background): “H ◦K corresponds to the classical ‘isotropic’ total variation (TV) [10,24], with H = 0.”