Analyzing the Sample Complexity of Self-Supervised Image Reconstruction Methods
This addresses the problem of limited clean data for image reconstruction tasks, providing a theoretical and empirical analysis of the trade-offs in self-supervised methods, though it is incremental in nature.
The paper analyzes the sample complexity of self-supervised image reconstruction methods, showing that while they achieve performance comparable to supervised training, they require more training examples, with the gap vanishing as sample size increases at a problem-dependent rate.
Supervised training of deep neural networks on pairs of clean image and noisy measurement achieves state-of-the-art performance for many image reconstruction tasks, but such training pairs are difficult to collect. Self-supervised methods enable training based on noisy measurements only, without clean images. In this work, we investigate the cost of self-supervised training in terms of sample complexity for a class of self-supervised methods that enable the computation of unbiased estimates of gradients of the supervised loss, including noise2noise methods. We analytically show that a model trained with such self-supervised training is as good as the same model trained in a supervised fashion, but self-supervised training requires more examples than supervised training. We then study self-supervised denoising and accelerated MRI empirically and characterize the cost of self-supervised training in terms of the number of additional samples required, and find that the performance gap between self-supervised and supervised training vanishes as a function of the training examples, at a problem-dependent rate, as predicted by our theory.