Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition
Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition
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发表时间：
2021-06
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通讯作者：
Jiaming Liu;M. Salman Asif;B. Wohlberg;U. Kamilov
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作者：
Jiaming Liu;M. Salman Asif;B. Wohlberg;U. Kamilov
即插即用先验（PnP）和去噪正则化（RED）方法已被广泛用于利用预训练的深度去噪作为图像先验来求解逆问题。虽然这些算法的经验成像性能和理论收敛性能已经得到了广泛的研究，但它们的恢复性能尚未得到理论分析。我们通过展示如何通过假设这些方法的解位于深度神经网络的不动点附近来建立PnP/RED的理论恢复保证来解决这一差距。我们还提供了数值结果，比较了PnP/RED在压缩感知中的恢复性能与最近基于生成模型的压缩感知算法的恢复性能。我们的数值结果表明，与现有的最先进的方法相比，带有预训练的伪影去除网络的PnP提供了明显更好的结果。
The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.