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.

翻译：基于清晰图像与噪声测量值配对的深度神经网络监督训练在众多图像重建任务中达到最优性能，但此类训练配对通常难以采集。多种自监督方法仅基于噪声测量值即可进行训练，无需清晰图像。本研究通过刻画样本复杂度来探究自监督训练的成本。我们聚焦于一类能够计算监督损失梯度无偏估计的自监督方法（含噪声到噪声方法）。首先通过理论分析表明，采用此类自监督训练的模型与监督训练模型性能相当，但自监督训练所需的样本量更大。继而通过实验研究自监督去噪和加速MRI，依据所需额外样本数量来量化自监督训练成本，并发现如理论预测所示：以问题相关速率，自监督与监督训练之间的性能差距随训练样本量增加而消失。