基于深度学习的反演算法: 某些最新进展

doi:10.19596/j.cnki.1001-246x.8992

摘要/Abstract

摘要：

反问题在雷达和声呐探测、医学成像、无损探伤、地球物理勘探等许多领域具有广泛而重要的应用。然而在大多数情况下, 反问题是一个病态的不适定问题, 构造其稳定高效的反演算法极具挑战性。利用未知解的先验信息来构建恰当的正则化策略是应对上述挑战的重要方法之一。传统正则化方法的成功依赖于将未知解准确的先验信息显式地编码到反演算法当中, 但在实际计算中这往往是难以获取和实现的。随着近年来深度学习技术的发展, 直接从数据中学习未知解的先验信息成为了可能, 这将有助于发展高效稳定的反演算法。本文回顾了基于深度学习反演算法的一些最新进展, 重点介绍基于可学习正则化框架的反演算法。此外, 还总结了基于深度学习反演算法的优缺点, 并展望其未来的发展方向。

关键词: 反问题, 反散射问题, 深度学习, 正则化方法, 可学习正则化框架

Abstract:

Inverse problems are of wide and important applications in many areas such as radar and sonar, medical imaging, nondestructive testing and geophysical prospection. Inverse problems are ill-posed problems, so it is challenging to construct stable and highly effective inversion algorithms for them. One of the important methods to tackle this challenging issue is to devise an appropriate regularization strategy based on the a priori information of the unknown solution. The success of traditional regularization methods heavily depends on correctly encoding the a priori information of the unknown solution into the inversion algorithms, but this is in general very difficult in practical computation. With the development of deep learning techniques in recent years, it becomes possible to directly learn the a priori information of the unknown solutions of the inverse problems from data, which is helpful in developing highly effective and stable inversion algorithms. In this paper, we review some recent progres on inversion algorithms based on deep learning, focusing mainly on those based on learnable regularization framework. In addition, we also summarize the advantages and shortcomings of the inversion algorithms based on deep learning, and discuss their future research directions.

Key words: inverse problems, inverse scattering, deep learning, regularization method, learnable regularization framework

李凯, 张波. 基于深度学习的反演算法: 某些最新进展[J]. 计算物理, 2024, 41(6): 717-731.

Kai LI, Bo ZHANG. Inversion Algorithms Based on Deep Learning for Inverse Problems: Some Recent Progresses[J]. Chinese Journal of Computational Physics, 2024, 41(6): 717-731.

图/表 5

图1 NPDHG-CSNet的网络结构

Fig.1 Network architecture of NPDHG-CSNet

图2 NPDHG-CSNet在不同采样率和笛卡尔掩膜下的MRI重构结果

Fig.2 Reconstructed MRI images of NPDHG-CSNet under different sampling rates and the Cartesian sampling mask

图3 投影迭代算法的流程图

Fig.3 Diagram of the projected iterative algorithm

图4 可学习投影迭代算法的重构结果(第3列) (a)Landweber; (b) simplified learned projected scheme; (c) learned projected scheme; (d) ground truth

Fig.4 Reconstructed results by learned projected iterative algorithm (3rd column) (a)Landweber; (b) simplified learned projected scheme; (c) learned projected scheme; (d) ground truth

图5 可学习投影迭代算法的泛化性能(a)Landweber; (b)learned projected algorithm; (c) ground truth

Fig.5 Generalization ability of learned projected iterative algorithm (a)Landweber; (b)learned projected algorithm; (c) ground truth

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