mlsanityData to 7 Oct 2026

Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equation

arXiv 2404.13866 ↗First posted 22 Apr 2024cs.CV math.PRcited by 0

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Abstract (arXiv)

The Plug-and-Play (PnP) algorithm is popular for inverse image problem-solving. However, this algorithm lacks theoretical analysis of its convergence with more advanced plug-in denoisers. We demonstrate that discrete PnP iteration can be described by a continuous stochastic differential equation (SDE). We can also achieve this transformation through Markov process formulation of PnP. Then, we can take a higher standpoint of PnP algorithms from stochastic differential equations, and give a unified framework for the convergence property of PnP according to the solvability condition of its corresponding SDE. We reveal that a much weaker condition, bounded denoiser with Lipschitz continuous measurement function would be enough for its convergence guarantee, instead of previous Lipschitz continuous denoiser condition.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 14 of its 33 references that are in the map. First posted on arXiv 22 Apr 2024.

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14 of 33 references.

References · 14

  1. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  2. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 407
  3. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  4. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  5. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  6. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 102
  7. 2018Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholdscited by 83
  8. 2018Denoising Prior Driven Deep Neural Network for Image Restorationcited by 80
  9. 2015Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolationcited by 78
  10. 2014Deep Unfolding: Model-Based Inspiration of Novel Deep Architecturescited by 76
  11. 2017Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibriumcited by 58
  12. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
2 more
  1. 2022On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descentcited by 14
  2. 2015Local Linear Convergence of ISTA and FISTA on the LASSO Problemcited by 8

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