Sparsity-Enhanced Multilayered Non-Convex Regularization with Epigraphical Relaxation for Debiased Signal Recovery

These are demo programs for the epigraphically-relaxed linearly-involved generalized Moreau-enhanced model (ER-LiGME model) proposed in the following reference:

A. Katsuma, S. Kyochi, S. Ono, I. Selesnick, "Sparsity-Enhanced Multilayered Non-Convex Regularization with Epigraphical Relaxation for Debiased Signal Recovery", 2024.

For more details, see the following

• Preprint paper: https://arxiv.org/abs/2409.14768

**Note: When downloading this code as a zip file, if you encounter the error '0x80010135: Path too long,' please use 7-Zip to extract the files or shorten the zip filename.

How to use

1) Prepare test images

• Place image files in the /images directory.
• Example: The Berkeley Segmentation Dataset

2) Edit parameters in demo_*.m

• Set the path to target image files
• Set the strength of noise
• Adjust the regularization parameters
  • Details for each parameter are explained in the code comments and the referenced paper.

3) Run demo_*.m

• for image denoising:
  • demo_denoising.m
• for compressed image sensing reconstruction:
  • demo_CSR.m,
  • demo_CSR_single.m (single precision)
• for principal component analysis of shifted signals:
  • demo_FRPCA.m

Citation

If you use this code, please cite the following paper:

@misc{katsuma2024sparsityenhancedmultilayerednonconvexregularization,
      title={Sparsity-Enhanced Multilayered Non-Convex Regularization with Epigraphical Relaxation for Debiased Signal Recovery}, 
      author={Akari Katsuma and Seisuke Kyochi and Shunsuke Ono and Ivan Selesnick},
      year={2024},
      eprint={2409.14768},
      archivePrefix={arXiv},
      primaryClass={eess.SP},
      url={https://arxiv.org/abs/2409.14768}, 
}