基于深度神经网络的速率最优去噪
Rate-Optimal Denoising with Deep Neural Networks
摘要：
深度神经网络为图像去噪提供了最先进的性能，其目标是从嘈杂的观察中恢复接近无噪声的图像。其基本原理是，在大型数据集上训练的神经网络已经被经验证明能够从图像的低维潜在表示很好地生成自然图像。给定这样的生成器网络，可以通过i）在生成器的范围内找到最接近的图像或ii）将其通过编码器-生成器架构（称为自动编码器）来对噪声图像进行降噪。然而，几乎没有理论来证明这一成功，更不用说预测作为网络参数的函数的去噪性能了。在本文中，我们考虑的问题，从加性高斯噪声的图像去噪使用两个发电机为基础的方法。在这两种情况下，我们假设图像由具有ReLU激活函数的深度神经网络很好地描述，将$k$维代码映射到$n$维图像。在自动编码器的情况下，我们表明，前馈网络降低噪声能量的一个因素的$O(k/n)$。在生成模型的范围内进行优化的情况下，我们陈述并分析了一个简单的梯度算法，该算法使非凸损失函数最小化，并可证明地将噪声能量降低了$O(k/n)$的因子。我们还在数值实验中证明，这种去噪性能确实是通过从数据中学习的生成先验来实现的。
英文摘要：
Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large datasets have empirically been shown to be able to generate natural images well from a low-dimensional latent representation of the image. Given such a generator network, a noisy image can be denoised by i) finding the closest image in the range of the generator or by ii) passing it through an encoder-generator architecture (known as an autoencoder). However, there is little theory to justify this success, let alone to predict the denoising performance as a function of the network parameters. In this paper we consider the problem of denoising an image from additive Gaussian noise using the two generator based approaches. In both cases, we assume the image is well described by a deep neural network with ReLU activations functions, mapping a $k$-dimensional code to an $n$-dimensional image. In the case of the autoencoder, we show that the feedforward network reduces noise energy by a factor of $O(k/n)$. In the case of optimizing over the range of a generative model, we state and analyze a simple gradient algorithm that minimizes a non-convex loss function, and provably reduces noise energy by a factor of $O(k/n)$. We also demonstrate in numerical experiments that this denoising performance is, indeed, achieved by generative priors learned from data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
