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.

本文提出了通过非线性特征值分析来分析黑盒图像去噪器的稳定模式和不稳定模式。我们旨在找到降噪输出与输入成比例的输入图像。我们将此视为广义非线性本征问题。潜在的影响是广泛的，因为大多数图像处理算法都可以看作是黑盒运算符。我们引入了广义非线性幂方法来解决此类算子的本征问题。这使我们能够揭示出降噪器的稳定模式：最佳输入，从而在噪声去除方面实现了卓越的PSNR。类似于线性情况，这种稳定模式显示出粗糙的结构并对应于大特征值。我们还提供了一种生成不稳定模式的方法，该模式会被降噪器强烈抑制，这是具有较小特征值的纹理。我们使用总变分（TV）验证了该方法，并在EPLL（Zoran–Weiss）和非局部均值降噪器上进行了证明。最后，我们建议使用加密解密应用程序。