Adrien Besson1 and Matthieu Simeoni2, February 2024
1E-Scopics, France
2Center for Imaging, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Code used to reproduce the results presented in the paper entitled New Perspectives on Generalized Finite Rate of Innovation, submitted to IEEE Signal Processing Letters
The generalized finite rate of innovation~(GenFRI) framework aims at reconstructing finite-rate-of-innovation~(FRI) signals measured through a noisy linear measurement model. GenFRI has been recently recast as a structured low-rank optimization problem and the Cadzow projected gradient descent~(CPGD) algorithm has been suggested to solve it. While CPGD works well in practice, only local convergence guarantees have been established.We introduce a different view of GenFRI under the light of the regularization by denoising~(RED) framework. We recast GenFRI as a RED optimization problem in which a solution lies in the fixed-point set of the Cadzow denoiser. We propose the generalized CPGD~(GCPGD) algorithm, a variant of CPGD which comes with stronger convergence guarantees. We show through numerical simulations that GCPGD outperforms state-of-the-art GenFRI algorithms.
- Python environment (Tested on 3.10)
- Python packages: numpy, scipy, matplotlib, joblib
You can download a copy of all the files in this repository by cloning the git repository:
git clone https://github.com/AdriBesson/gcpgd.git
- If you want to reproduce the experiments, run one of the following scripts
reproduce_lipschitz_cadzow.py
reproduces the results of the Section IV.A entitled "Lipschitz Constant of Cadzow Denoising"reproduce_simulation_results.py
reproduces the results of the Section IV.B entitled "Reconstruction Accuracy of GCPGD"
Adrien Besson ([email protected])
Please cite the following paper when using the code: A. Besson and M. Siméoni, "New Perspectives on Generalized Finite Rate of Innovation", submitted to IEEE Signal Processing Letters, 2024.
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Copyright (c) 2020 Matthieu SIMEONI, Adrien BESSON, Paul HURLEY and Martin VETTERLI
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