【信号去噪】基于柯西近端分裂 (CPS) 算法实现信号去噪附MATLAB源代码.zip

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 <[email protected]> and Alin Achim <[email protected]>, 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 *****************************************************************************************************************