Revealing Stable and Unstable Modes of Generic Denoisers through Nonlinear Eigenvalue Analysis
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.
Code (0)
등록된 구현이 없습니다.
Tasks
DenoisingSimilar Papers 제목 키워드 기반
Stabilizing Linear Systems under Partial Observability: Sample Complexity and Fundamental Limits
We study the problem of stabilizing an unknown partially observable linear time-invariant (LTI) system. For fully observable systems, leveraging an unstable/stable subspace decomposition approach, state-of-art sample com…
Spectral Dynamics of Learning Restricted Boltzmann Machines
The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical o…
System stabilization with policy optimization on unstable latent manifolds
Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time…
reinforcement-learningReinforcement LearningLearning Stabilizing Policies via an Unstable Subspace Representation
We study the problem of learning to stabilize (LTS) a linear time-invariant (LTI) system. Policy gradient (PG) methods for control assume access to an initial stabilizing policy. However, designing such a policy for an u…
Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching
For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected fr…