gaobian / chambollepock

A Python implementation of the Chambolle-Pock algorithm for image processing applications examples

Chambolle-Pock algorithm for Total Variation minimization

This repository is a Python implementation of the Chambolle-Pock algorithm [1] for minimizing an objective function with Total Variation (TV) regularization. It is mainly written for a didactic purpose.

Two examples are implemented :

• Deconvolution
• Tomographic reconstruction

There is also an implementation of conjugate gradient using a smoothed TV described in [2].

Installation

Simply download and execute the sample scripts. For tomographic reconstruction, the ASTRA toolbox version 1.6 should be installed beforehand.

Usage

The file CP.py implements the Chambolle-Pock algorithm for minimizing

where K can be any linear operator (here, convolution or tomographic projection).

The file CG.py implements a conjugate gradient algorithm for solving the previous problem, where the TV is approximated by

with

Both of these files can be executed.

The other files contain functions implementing various operators.

[1] Antonin Chambolle, Thomas Pock, A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging, 2011, Journal of Mathematical Imaging and Vision, Vol. 40 Issue 1, pp. 120-145

[2] Pierre Weiss, Laure Blanc-Féraud, and Gilles Aubert, Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, 2008, SIAM J. Sci. Comput., 31(3), 2047–2080