Compressed Sensing with Deep Image Prior and Learned Regularization
Dave Van Veen Ajil Jalal Mahdi Soltanolkotabi Eric Price Sriram Vishwanath Alexandros G. Dimakis Equal contributionDepartment of Electrical and Computer Engineering, University of Texas. Austin, TXDepartment of Electrical Engineering, University of Southern California. Los Angeles, CADepartment of Computer Science, University of Texas. Austin, TX
Abstract
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 nonconvex nature of the fitting problem. This theoretical result provides justification for early stopping.
中文速览
用未经预训练的深度生成网络也能做压缩感知（Compressed Sensing）重建——这篇论文把"深度图像先验"（Deep Image Prior，DIP）引入压缩感知任务，用一个随机初始化的卷积网络（DCGAN）直接对网络权重做梯度下降，让网络输出与观测测量值吻合，从而恢复未知图像，完全不需要在大规模数据集上预训练生成模型。为了进一步压低重建误差（尤其是在噪声较大时），作者还设计了一种"学习正则化"方法：先用少量同类图像的测量值估计网络权重的高斯先验分布，再把这个先验作为正则项约束当前优化，相当于自适应的权重衰减。理论上，作者证明了对单隐层适度过参数化网络，梯度下降必然能将任意信号拟合到零误差，这为实践中常用的"早停"策略提供了严格的理论依据。实验表明，该方法在多种医学成像数据集上超越了BM3D-AMP、TVAL3等经典无学习方法，对那些难以收集大量训练数据的医疗场景尤具实用价值。
原文 arXiv:1806.06438;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1806.06438v4