One Size Fits All: Can We Train One Denoiser for All Noise Levels?

TL;DR

This paper investigates the optimal training sample distribution for neural network denoisers across noise levels, proposing a minimax risk approach and a dual ascent algorithm to improve generalization.

Contribution

It introduces a novel minimax risk-based framework and a dual ascent algorithm to optimize training sample distributions for denoising models.

Findings

The dual ascent algorithm converges for convex estimator sets.

Optimal sampling distributions differ from uniform, favoring less noisy samples.

The approach improves denoising performance across noise levels.

Abstract

When training an estimator such as a neural network for tasks like image denoising, it is often preferred to train one estimator and apply it to all noise levels. The de facto training protocol to achieve this goal is to train the estimator with noisy samples whose noise levels are uniformly distributed across the range of interest. However, why should we allocate the samples uniformly? Can we have more training samples that are less noisy, and fewer samples that are more noisy? What is the optimal distribution? How do we obtain such a distribution? The goal of this paper is to address this training sample distribution problem from a minimax risk optimization perspective. We derive a dual ascent algorithm to determine the optimal sampling distribution of which the convergence is guaranteed as long as the set of admissible estimators is closed and convex. For estimators with non-convex admissible sets such as deep neural networks, our dual formulation converges to a solution of the convex relaxation. We discuss how the algorithm can be implemented in practice. We evaluate the algorithm on linear estimators and deep networks.