Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators
Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators
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发表时间：
2019-10
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通讯作者：
Reinhard Heckel;M. Soltanolkotabi
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作者：
Reinhard Heckel;M. Soltanolkotabi
卷积神经网络（CNN）已经成为图像生成，恢复和恢复的非常成功的工具。这种成功通常归功于大量的训练数据。然而，最近的实验结果挑战了这一观点，相反，这一成功的一个主要因素是卷积网络对自然图像施加了强有力的先验假设。一个令人惊讶的实验强调了这种对自然图像的建筑偏见，即可以在不使用任何训练数据的情况下从自然图像中去除噪声和损坏，只需将随机初始化的，过度参数化的卷积生成器拟合（通过梯度下降）到单个损坏的图像。虽然这种过度参数化的网络可以完美地拟合损坏的图像，但令人惊讶的是，经过几次梯度下降迭代后，人们获得了未损坏的图像。这种有趣的现象使最先进的基于CNN的去噪和线性逆问题的正则化成为可能，例如压缩感知。在本文中，我们通过将这种效应归因于卷积网络的特定架构选择，即具有固定插值滤波器的卷积，从而朝着揭开这种实验现象的神秘性迈出了一步。然后，我们正式描述了将两层卷积生成器拟合到噪声信号的动态特性，并证明了早期停止的梯度下降去噪/正则化。这一结果依赖于卷积生成器对图像结构化部分的拟合速度明显快于损坏部分。
Convolutional Neural Networks (CNNs) have emerged as highly successful tools for image generation, recovery, and restoration. This success is often attributed to large amounts of training data. However, recent experimental findings challenge this view and instead suggest that a major contributing factor to this success is that convolutional networks impose strong prior assumptions about natural images. A surprising experiment that highlights this architectural bias towards natural images is that one can remove noise and corruptions from a natural image without using any training data, by simply fitting (via gradient descent) a randomly initialized, over-parameterized convolutional generator to the single corrupted image. While this over-parameterized network can fit the corrupted image perfectly, surprisingly after a few iterations of gradient descent one obtains the uncorrupted image. This intriguing phenomenon enables state-of-the-art CNN-based denoising and regularization of linear inverse problems such as compressive sensing. In this paper, we take a step towards demystifying this experimental phenomenon by attributing this effect to particular architectural choices of convolutional networks, namely convolutions with fixed interpolating filters. We then formally characterize the dynamics of fitting a two-layer convolutional generator to a noisy signal and prove that early-stopped gradient descent denoises/regularizes. This result relies on showing that convolutional generators fit the structured part of an image significantly faster than the corrupted portion.