We propose a novel method for compressed sensing recovery using untrained
deep generative models. Our method is based on the recently proposed Deep Image
Prior (DIP), wherein the convolutional weights of the network are optimized to
match the observed measurements. We show that this approach can be applied to
solve any differentiable linear inverse problem, outperforming previous
unlearned methods. Unlike various learned approaches based on generative
models, our method does not require pre-training over large datasets. We
further introduce a novel learned regularization technique, which incorporates
prior information on the network weights. This reduces reconstruction error,
especially for noisy measurements. Finally, we prove that, using the DIP
optimization approach, moderately overparameterized single-layer networks can
perfectly fit any signal despite the non-convex nature of the fitting problem.
This theoretical result provides justification for early stopping.

通过未经训练的深度生成模型提出一种新方法，解决压缩感知恢复问题，具有比以前的方法更好的性能，并且不需要大规模数据集的预训练。同时，结合了关于网络权重的先验知识的新型学习正则技术，减少了重建误差。最后，通过 DIP 优化方法，证明了适度超参数的单层神经网络可以完美拟合任何信号，这一理论结果为提前停止提供了依据。