SUNLayer: Stable denoising with generative networks
This work provides a theoretical foundation for understanding generative models in denoising, which is incremental as it builds on existing methods with a new analytical approach.
The paper tackles the problem of analyzing generative models for denoising by introducing SUNLayer, a theoretical framework based on spherical harmonics that identifies conditions on activation functions to guarantee denoising under local optimization, with numerical experiments demonstrating stable performance.
Deep neural networks are often used to implement powerful generative models for real-world data. Notable applications include image denoising, as well as other classical inverse problems like compressed sensing and super-resolution. To provide a rigorous but simplified analysis of generative models, in this work, we introduce an elegant theoretical framework based on spherical harmonics, namely \textbf{SUNLayer}. Our theoretical framework identifies explicit conditions on activation functions that guarantee denoising under local optimization. Numerical experiments examine the theoretical properties on commonly used activation functions and demonstrate their stable denoising performance.