This source code package includes the MATLAB source codes for the Cauchy proximal splitting algorithm.
These Matlab functions implement a proximal splitting method involving a non-convex penalty function based on the heavy-tailed Cauchy distribution. A function for calculating the proximal operator of the Cauchy prior is provided, and two examples are included to illustrate how to perform cost function optimisation with a forward-backward (FB) -based algorithm that implements the corresponding Cauchy proximal splitting (CPS) method. The two signal processing examples include 1D signal denoising in the frequency domain and image de-blurring.
This package includes three MATLAB scripts:
1) CauchyProx : The MATLAB function that performs the proximal operator operation for the Cauchy penalty function.
2) CPS_1D_denoising : An example code for 1D signal denoising via the Cauchy proximal splitting algorithm.
3) CPS_2D_deblurring : An example code for 2D image deblurring via the Cauchy proximal splitting algorithm.
LICENSE
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.
Copyright (C) Oktay Karakus o.karakus@bristol.ac.uk and Alin Achim alin.achim@bristol.ac.uk, 12-05-2020, University of Bristol, UK
REFERENCE
[1] O Karakus, P Mayo, and A Achim. "Convergence Guarantees for Non-Convex Optimisation with Cauchy-Based Penalties" IEEE Transactions on Signal Processing 68 (2020): 6159-6170.
https://arxiv.org/abs/2003.04798
[2] O Karakus, A Achim. (2020): Cauchy Proximal Splitting (CPS).
https://doi.org/10.5523/bris.15y437loa26cr2nx8gnn3l4hzi