无需训练数据,用随机初始化网络修复图像,突破医疗成像等场景限制。
Understanding Untrained Deep Models for Inverse Problems: Algorithms and Theory
- 用随机初始化的卷积网络直接从噪声中重建图像,不依赖外部数据集。
- 理论分析揭示其训练动态,解释为何能避免过拟合并恢复结构细节。
- 结合预训练模型与早停策略,提升稳定性,适合数据稀缺领域应用。
近年来,深度学习在逆成像问题(IIPs)中广泛应用,涵盖监督、自监督和生成式方法。多数方法需大量标注或无标注训练数据,但在医学图像重建等实际场景中,高质量数据往往难以获取。2018年,Ulyanov等人提出的深度图像先验(Deep Image Prior, DIP)首次实现无需训练数据的神经网络方法。DIP仅需卷积网络、噪声观测值和前向算子,通过随机初始化网络的隐式正则化能力,在无外部数据情况下恢复图像结构。然而,其主要局限是因网络过参数化易导致过拟合。本文综述DIP及其理论分析,分类讨论近期缓解过拟合的方法,如正则化、重参数化与早停;同时探讨结合预训练网络的方案,对比数据驱动方法的实验结果,并指出开放性问题与未来方向。
原文摘要 · Abstract (English)
In recent years, deep learning methods have been extensively developed for inverse imaging problems (IIPs), encompassing supervised, self-supervised, and generative approaches. Most of these methods require large amounts of labeled or unlabeled training data to learn effective models. However, in many practical applications, such as medical image reconstruction, extensive training datasets are often unavailable or limited. A significant milestone in addressing this challenge came in 2018 with the work of Ulyanov et al., which introduced the Deep Image Prior (DIP)--the first training-data-free neural network method for IIPs. Unlike conventional deep learning approaches, DIP requires only a convolutional neural network, the noisy measurements, and a forward operator. By leveraging the implicit regularization of deep networks initialized with random noise, DIP can learn and restore image structures without relying on external datasets. However, a well-known limitation of DIP is its susceptibility to overfitting, primarily due to the over-parameterization of the network. In this tutorial paper, we provide a comprehensive review of DIP, including a theoretical analysis of its training dynamics. We also categorize and discuss recent advancements in DIP-based methods aimed at mitigating overfitting, including techniques such as regularization, network re-parameterization, and early stopping. Furthermore, we discuss approaches that combine DIP with pre-trained neural networks, present empirical comparison results against data-centric methods, and highlight open research questions and future directions.
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