基于压缩感知的脉冲星信号恢复和天文去卷积

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.

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。

本项目采用压缩感知(CS)理念，突破了传统的奈奎斯特(Nyqusit)采样定理的局限，将其应用于射电脉冲星数据去噪和恢复、射电星系宇宙学图像去卷积、射电源源检测中。当前国内CS方法在天文数据处理领域逐渐展开，但是无论广度和深度较之国际发达国家还不够，本项目致力于打造中国天文数据CS应用研究的部分先驱工作。在脉冲星数据去噪和恢复方面，在CS优化框架下使用ISTA和FISTA等数值算法，并使用以Curvelet为代表的多种稀疏算子，然后使用迭代式Curvelet阈值算法。星系宇宙学数据去卷积的理论中，创新性的提出形状约束的概念。并将方向字典和各向同性小波联合使用，创建一种联合字典，对于射电源数据的各向同性和各向异性信息同时进行稀疏表示。并使用Proximal Calculus的理论和加速算法，得到理想结果。射电源检测和追踪使用Level Set水平集方法和主动轮廓,并在CS框架下采用边界信息提取和图像重建相结合的方式，使得迭代中两者交替工作，相互促进。此种理念对于回收每一迭代的边界信息极其有利。创新性在于，我们寻找一条关于CS和主动轮廓相结合的新道路，这是通过将CS测度作为轮廓演化的“驱动力”来完成的。本项目将CS理念创新性地应用于具有代表性的天文数据的处理中，符合当前国际天文信号处理领域的新趋势，顺应我国天文新时代的新要求，对于天文技术应用研究具有一定意义。