论文标题
基于深度学习的图像重建的缩放定律
Scaling Laws For Deep Learning Based Image Reconstruction
论文作者
论文摘要
深度神经网络端到端训练的深度神经网络将（嘈杂）图像映射到干净的图像的测量值非常适合各种线性反问题。当前的方法仅在数百或数千个图像上进行训练，而不是在其他领域中对深网进行了培训。在这项工作中，我们研究是否可以通过扩大训练套件的规模来获得重大的性能增长。我们考虑图像降解，加速磁共振成像以及超分辨率，并经验确定重建质量是训练集大小的函数，同时缩放网络大小。对于这三个任务，我们发现最初陡峭的幂律缩放率已经在适度的训练集大小上大大减慢。插值这些缩放定律表明，即使对数百万图像进行培训也不会显着提高性能。为了了解预期的行为，我们分析表征了以早期停止梯度下降学到的线性估计器的性能。结果正式的直觉是，一旦通过学习信号模型引起的误差，相对于误差地板而言，更多的训练示例不会提高性能。
Deep neural networks trained end-to-end to map a measurement of a (noisy) image to a clean image perform excellent for a variety of linear inverse problems. Current methods are only trained on a few hundreds or thousands of images as opposed to the millions of examples deep networks are trained on in other domains. In this work, we study whether major performance gains are expected from scaling up the training set size. We consider image denoising, accelerated magnetic resonance imaging, and super-resolution and empirically determine the reconstruction quality as a function of training set size, while simultaneously scaling the network size. For all three tasks we find that an initially steep power-law scaling slows significantly already at moderate training set sizes. Interpolating those scaling laws suggests that even training on millions of images would not significantly improve performance. To understand the expected behavior, we analytically characterize the performance of a linear estimator learned with early stopped gradient descent. The result formalizes the intuition that once the error induced by learning the signal model is small relative to the error floor, more training examples do not improve performance.
