Revealing stable and unstable modes of denoisers through nonlinear eigenvalue analysis

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.