[Paper Review] Variational Denoising Network: Toward Blind Noise Modeling and Removal

Zongsheng Yue, Hongwei Yong+3 more|arXiv (Cornell University)|Aug 29, 2019

Image and Signal Denoising Methods212 citations

TL;DR

The paper introduces Variational Denoising Network (VDN), a Bayesian variational inference framework that jointly estimates the latent clean image and a non-i.i.d. noise distribution from a single noisy image for blind denoising, implemented with a D-Net and an S-Net.

ABSTRACT

Blind image denoising is an important yet very challenging problem in computer vision due to the complicated acquisition process of real images. In this work we propose a new variational inference method, which integrates both noise estimation and image denoising into a unique Bayesian framework, for blind image denoising. Specifically, an approximate posterior, parameterized by deep neural networks, is presented by taking the intrinsic clean image and noise variances as latent variables conditioned on the input noisy image. This posterior provides explicit parametric forms for all its involved hyper-parameters, and thus can be easily implemented for blind image denoising with automatic noise estimation for the test noisy image. On one hand, as other data-driven deep learning methods, our method, namely variational denoising network (VDN), can perform denoising efficiently due to its explicit form of posterior expression. On the other hand, VDN inherits the advantages of traditional model-driven approaches, especially the good generalization capability of generative models. VDN has good interpretability and can be flexibly utilized to estimate and remove complicated non-i.i.d. noise collected in real scenarios. Comprehensive experiments are performed to substantiate the superiority of our method in blind image denoising.

Motivation & Objective

• Motivate and address blind image denoising where real-world noise is non-i.i.d. and hard to predefine.
• Propose a full Bayesian model that treats the clean image and per-pixel noise variances as latent variables.
• Develop a variational inference framework yielding an explicit posterior for robust inference and noise estimation.
• Demonstrate broad generalization to complex noise distributions beyond training data.

Proposed method

• Formulate y_i ~ N(z_i, sigma_i^2) with non-i.i.d. pixelwise Gaussian noise.
• Assume z_i ~ N(x_i, epsilon_0^2) using a simulated clean image x as prior.
• Place sigma_i^2 ~ IG(p^2/2 - 1, p^2 xi_i/2) with xi_i from a Gaussian-filtered variance map.
• Adopt a variational posterior q(z|y) and q(sigma^2|y) with D-Net and S-Net predicting mu_i, m_i^2, alpha_i, beta_i.
• Maximize a tractable variational lower bound of log p(y) leading to an end-to-end training objective.
• At test time, output denoised image as mu from D-Net and inferred noise variances from S-Net.

Experimental results

Research questions

• RQ1 Can a unified Bayesian framework jointly denoise and estimate spatially varying noise without knowing the exact noise model a priori?
• RQ2 Does a variational approach with explicit posterior forms improve generalization to unseen non-i.i.d. noise compared to conventional CNN denoisers?
• RQ3 How well can a D-Net/S-Net architecture recover both latent clean images and pixelwise noise variances from a single noisy image?
• RQ4 Does explicit noise modeling provide interpretable noise maps and robust denoising across synthetic and real-world datasets?

Key findings

• VDN outperforms competing methods on synthetic non-i.i.d. Gaussian noise across multiple test sets.
• VDN achieves higher PSNR than FFDNet on non-i.i.d. noise and shows less overfitting to training noise biases.
• VDN yields competitive or superior results on real-world benchmarks SIDD and DND after training on a mixture dataset.
• The S-Net can predict a plausible noise variance map that correlates with image content and realism of noise.
• The framework remains robust under AWGN and supports interpretability via the inferred noise variance statistics.
• A degenerate MSE loss arises if epsilon_0^2 is set very small, explaining overfitting in purely discriminative models.