Revealing Stable and Unstable Modes of Generic Denoisers through Nonlinear Eigenvalue Analysis
This provides insights into the behavior of nonlinear denoisers, which are widely used in image processing, but the approach is incremental as it extends linear eigenvalue concepts to nonlinear operators.
The paper tackles the problem of analyzing stable and unstable modes in generic image denoisers by formulating it as a nonlinear eigenvalue problem, resulting in a method that reveals optimal inputs for superior PSNR in noise removal and generates complementary unstable modes.
In this paper, we propose to analyze stable and unstable modes of generic image denoisers through nonlinear eigenvalue analysis. We attempt to find input images for which the output of a black-box denoiser is proportional to the input. We treat this as a nonlinear eigenvalue problem. This has potentially wide implications, since most image processing algorithms can be viewed as generic nonlinear operators. We introduce a generalized nonlinear power-method to solve eigenproblems for such black-box operators. Using this method we reveal stable modes of nonlinear denoisers. These modes are optimal inputs for the denoiser, achieving superior PSNR in noise removal. Analogously to the linear case (low-pass-filter), such stable modes are eigenfunctions corresponding to large eigenvalues, characterized by large piece-wise-smooth structures. We also provide a method to generate the complementary, most unstable modes, which the denoiser suppresses strongly. These modes are textures with small eigenvalues. We validate the method using total-variation (TV) and demonstrate it on the EPLL denoiser (Zoran-Weiss). Finally, we suggest an encryption-decryption application.