Online Deep Equilibrium Learning for Regularization by Denoising
Online Deep Equilibrium Learning for Regularization by Denoising
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DOI：
10.48550/arxiv.2205.13051
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Jiaming Liu;Xiaojian Xu;Weijie Gan;S. Shoushtari;U. Kamilov
中科院分区：
文献类型：
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作者：
Jiaming Liu;Xiaojian Xu;Weijie Gan;S. Shoushtari;U. Kamilov
即插即用先验（Plug-and-Play Priors，PPENS）和去噪正则化（Regularization by Denoising，RED）是通过计算结合物理测量模型和学习的图像先验的算子的不动点来解决成像逆问题的广泛使用的框架。虽然传统的PADER/RED公式集中在使用图像去噪器指定的先验上，但人们对学习端到端最佳的PADER/RED先验的兴趣越来越大。最近的深度均衡模型（DEQ）框架通过隐式差分定点方程，实现了PPENDIX/RED先验的存储高效的端到端学习，而无需存储中间激活值。然而，依赖的计算/存储器的复杂性的测量模型在PPENS/RED的测量总数离开DEQ不切实际的许多成像应用。我们提出ODER作为一种新的策略，通过随机近似的测量模型，提高效率的DEQ。我们从理论上分析了ODER，深入了解其收敛性和逼近传统DEQ方法的能力。我们的数值结果表明，由于ODER在三个不同的成像应用中的训练/测试复杂性的潜在改进。
Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) are widely-used frameworks for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image priors. While traditional PnP/RED formulations have focused on priors specified using image denoisers, there is a growing interest in learning PnP/RED priors that are end-to-end optimal. The recent Deep Equilibrium Models (DEQ) framework has enabled memory-efficient end-to-end learning of PnP/RED priors by implicitly differentiating through the fixed-point equations without storing intermediate activation values. However, the dependence of the computational/memory complexity of the measurement models in PnP/RED on the total number of measurements leaves DEQ impractical for many imaging applications. We propose ODER as a new strategy for improving the efficiency of DEQ through stochastic approximations of the measurement models. We theoretically analyze ODER giving insights into its convergence and ability to approximate the traditional DEQ approach. Our numerical results suggest the potential improvements in training/testing complexity due to ODER on three distinct imaging applications.