Revealing stable and unstable modes of denoisers through nonlinear eigenvalue analysis

Ester Hait-Fraenkel, Guy Gilboa

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose to analyze stable and unstable modes of black-box image denoisers through nonlinear eigenvalue analysis. We aim to find input images for which the denoiser output is proportional to the input. We treat this as a generalized nonlinear eigenproblem. Potential implications are wide, as most image processing algorithms can be viewed as black-box operators. We introduce a generalized nonlinear power-method to solve eigenproblems for such operators. This allows us to reveal stable modes of the denoiser: optimal inputs, achieving superior PSNR in noise removal. Analogously to the linear case, such stable modes show coarse structures and correspond to large eigenvalues. We also provide a method to generate unstable modes, which the denoiser suppresses strongly, which are textural with small eigenvalues. We validate the method using total-variation (TV) and demonstrate it on the EPLL (Zoran–Weiss) and the Non-local means denoisers. Finally, we suggest an encryption–decryption application.

Original languageEnglish
Article number103041
JournalJournal of Visual Communication and Image Representation
Volume75
DOIs
StatePublished - Feb 2021

Keywords

  • Denoising
  • EPLL
  • Eigenfunctions
  • Nonlinear operators
  • Power iteration
  • Total-variation

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Media Technology
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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