压缩感知(CS)突破传统Shannon采样定理的“瓶颈”，其基本原则是稀疏或可压缩信号可以由远小于Nyquist抽样率的测度完全重建。国际上，CS已在信号处理的各个领域取得大的进展，然而对天文数据的应用研究却刚刚起步，在中国更少。CS大力应用于我国天文信号和图像领域已成为当务之急。本项目提出将CS应用于天文脉冲星数据识别和恢复，弱引力透镜数据去卷积的思想及一系列方法。它将对CS国际方法进行理论分析和革新，是理论创新；将国际主流方法多种框架应用于国内天文数据亟待解决的重要课题分支，是应用创新；以天文数据特征为主要对象，革新当前CS算法，是方法创新。本项目致力于将基于稀疏表示(如wavelet或curvelet)的CS、全变分标准化L1模型以及盲压缩感知(BCS)等框架应用于脉冲星信号、弱引力透镜场数据和宇宙微波背景辐射领域。重点研究缺失和变形信号和数据的恢复、去卷积等关键技术。

Compressed sensing (CS) has broken through the "bottleneck" of the traditional Shannon sampling theorem. Its basic principle is that sparse or compressible signal can be completely reconstructed from the measurements far less than the Nyquist sampling rate. Internationally, CS has made great progresses in various fields of signal processing, but the applied research for astronomical data has just started. In China, applications of CS in the astronomical signal processing are even fewer. It is a task of top priority for China to apply CS to the field of astronomical signal and image processing. This project will propose the ideas and a series of methods for CS based pulsar signal profile recognition and restoration, and weak lensing data deconvolution. It will make theoretical analysis and innovations for the currently used mainstream algorithms of CS, which is the theoretical innovation. It will apply a variety of CS frameworks in the important subject branches of astronomical data, which need to be solved urgently. This is the applicational innovation. This project will take the astronomical data features as the main object, reform the currently used CS algorithms. This is the methodological innovation. The project will devote itself to the applications of sparse representation (such as wavelet or curvelet) based CS, the total variation L1 model regularization and the blind compressed sensing (BCS) framework to the pulsar signal profiles, weak lensing data field and the cosmic microwave background(CMB). The key techniques are the recognition, restoration and deconvolution with missing or distorted signals and data.