深度学习框架下压缩感知的可解释重建方法研究

Compressed sensing based on deep learning is a milestone in the development of compressed sensing theory, which is driven by data, jointly optimizes the non-linear measurement network and the deep reconstruction network, so as to reduce the reconstruction time order of magnitude and improve the reconstruction accuracy significantly. However, the reconstructed network relies on a large amount of training data, and its performance decreases sharply in the case of small samples. The reconstruction network is a hard-to-understand black box, which hinders researchers from improving the CS system. The lack of interpretability of reconstruction also leads to users' distrust of the results of reconstruction. Aiming at the above problems, this project intends to study from three aspects: signal measurement, signal reconstruction and interpretation methods of reconstruction: 1) Through parallel strategy, a non-linear measurement network with fast and efficient acquisition of signal structure is designed to promote high-precision reconstruction at low measurement rate; 2) A priori knowledge is extracted from a small sample to construct the regularization term in the objective function, which can guide the parameter learning of the reconstruction network, and achieve high precision real-time reconstruction under a small sample; 3) Based on active learning and standardized flow strategy, an interpretable observation space is constructed, and the relationship between hidden layer and salient features of signals is constructed by collaborating domain experts, thus an interpretable mechanism for reconstructing networks is established. This project will reveal the characterization and reconstruction mechanism of compressed sensing network for signal structure, and promote the practical application of compressed sensing in medicine, remote sensing and other fields.

基于深度学习的压缩感知通过数据驱动，联合优化非线性测量网络和深度重建网络，使重建时间数量级减少、重建精度显著提高，是压缩感知理论的里程碑式进展。然而，重建网络依赖大量训练数据，在小样本情况下性能急剧下降；且重建网络是难以理解的黑盒，阻碍了研究者对重建系统的改进，重建可解释性的缺失也导致用户对重建结果的不信任。针对上述问题，本项目拟从信号测量、信号重建、重建的解释方法三方面研究：1)通过并行策略，设计能快速高效捕获信号结构的非线性测量网络，促进低测量率下的高精度重建；2)从小样本中抽取先验知识，以此构建目标函数中正则化项，指导重建网络的参数学习，实现小样本下高精度实时重建；3)基于主动学习和标准化流策略，构建可解释观测空间，协同领域专家构建网络隐层与信号显著特征的关系，从而建立重建网络的可解释机制。本项目将揭示压缩感知网络对信号结构的表征及重建机理，促进压缩感知在医学、遥感等领域的实际应用。

本项目针对重建网络依赖大量训练数据、重建可解释性缺失等问题，研究可解释压缩感知关键技术，主要内容包括：1)通过并行策略，设计能快速高效捕获信号结构的非线性测量网络，促进低测量率下的高精度重建；2)从小样本中抽取先验知识，以此构建目标函数中正则化项，指导重建网络的参数学习，实现小样本下高精度实时重建；3)基于主动学习和标准化流策略，构建可解释观测空间，协同领域专家构建网络隐层与信号显著特征的关系，从而建立重建网络的可解释机制。项目执行从信号测量、信号重建、重建的解释方法三个方面完成了如下工作。首先针对测量端对信号特征捕捉能力不够的问题，用全卷积网络测量替代分块测量方法以避免分块效应，将图像变换至小波域之后再用卷积层获取测量值，将测量与重建网络联合训练优化，达到低采样率下高效快速测量信号的目的。然后针对现有重建方法在训练样本不足情况下性能显著下降的问题，采用空洞卷积构建多通道的重建网络，通过注意力机制对重建的多个通道自适应分配不同权重，由对抗网络构建反馈机制，以优化重建网络架构，达到在小样本条件下高精度、实时重建信号的目的。最后针对重建方法可解释性缺失的问题，采用类激活映射的方法对网络层特性进行可视化及定量研究，并对有良好理论基础的传统算法进行展开，来实现高精度及可解释的重建网络。该项目能揭示压缩感知网络对信号结构的表征及重建机理，促进压缩感知在医学、遥感等领域的实际应用。项目执行期间以一作或通讯作者共计发表学术论文21篇（其中SCI收录论文5篇、EI收录论文13篇、核心期刊收录论文3篇）、授权发明专利2项、申请发明专利13项、获授权软件著作权6项、开发压缩感知图像重建平台2套、培养硕士研究生10名，完成项目计划书规定的各项任务。