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Cadzow Projected Gradient Descent for Generalized Finite Rate of Innovation: A Quantitative Local Convergence Theory — arXiv:2609.02921

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.02921
License (as archived): CC0-1.0
Archived: 2026-10-17T03:22:59.177Z
SHA-256 of the archived text: 09b025d79d6407788bc7dc4bfbb675b410ec54eb07c0155711ac230720b8e81f
Stable URL of this page: https://metraipolis.com/documento/dc_fdcd0401bd55

How to cite

Cadzow Projected Gradient Descent for Generalized Finite Rate of Innovation: A Quantitative Local Convergence Theory — arXiv:2609.02921 — arXiv (en), https://arxiv.org/abs/2609.02921 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fdcd0401bd55 (Metraipolis archive dc_fdcd0401bd55, sha256 09b025d79d6407788bc7dc4bfbb675b410ec54eb07c0155711ac230720b8e81f)

BibTeX

@misc{dcfdcd0401bd55,
  title = {Cadzow Projected Gradient Descent for Generalized Finite Rate of Innovation: A Quantitative Local Convergence Theory — arXiv:2609.02921},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.02921},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fdcd0401bd55; sha256 09b025d79d6407788bc7dc4bfbb675b410ec54eb07c0155711ac230720b8e81f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.02921. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 qualitative local convergence guarantees have been established. We revisit GenFRI in the light of the regularization by denoising framework, recasting it as an optimization problem whose solutions lie in the fixed-point set of the Cadzow denoiser. We show that no algorithm in this family can enjoy global guarantees, and establish instead that the Cadzow denoiser is quasi-nonexpansive on an explicit neighborhood of the FRI model set, whose radius is governed by the conditioning of the underlying Dirac stream. Building on these results, we propose the generalized CPGD~(GCPGD) algorithm and prove its convergence from any initialization within an explicit basin of attraction, together with a reconstruction error bound proportional to the noise level. Numerical experiments validate the predicted contraction rates, recovery thresholds, and run-time certificates, and show that a single run of GCPGD outperforms state-of-the-art GenFRI algorithms.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-04 in eess.SP).
Categorie arXiv: Signal Processing (eess.SP).
Pagina del lavoro: https://arxiv.org/abs/2609.02921 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T03:09:04.241Z dalla pagina https://arxiv.org/catchup/eess.SP/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).