Inversion Algorithms Based on Deep Learning for Inverse Problems: Some Recent Progresses

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

Abstract

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

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.

Figures/Tables 5

Fig.1 Network architecture of NPDHG-CSNet

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

Fig.3 Diagram of the projected iterative algorithm

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

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

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