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 usually difficult to collect. A variety of self-supervised methods enable training based on noisy measurements only, without clean images. In this work, we investigate the cost of self-supervised training by characterizing its sample complexity. We focus on a class of self-supervised methods that enable the computation of unbiased estimates of gradients of the supervised loss, including noise2noise methods. We first 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.

探究自监督训练方法的样本复杂度，发现模型的性能会随着训练样本数量增加而提高，证明采用自监督训练方法所需样本较多，但与监督训练方法优化模型的性能差距会随着样本数量增加而逐渐缩小。

自监督图像重建方法的样本复杂度分析