稀疏采样傅里叶望远镜成像  

Fourier telescopy imaging via sparse sampling

作　　者：刘欣悦[1] 董磊[1] 王建立[1] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所,吉林长春130033

出　　处：《光学精密工程》2010年第3期521-527,共7页Optics and Precision Engineering

基　　金：国家863高技术研究发展计划资助项目(No.2008AA7034250)

摘　　要：为了实现傅里叶望远镜快速成像,提出了一种稀疏采样图像重构方法,并对利用稀疏傅里叶样本精确重构目标图像的问题进行了研究。首先,基于压缩感知理论,并考虑目标图像在变换域的稀疏性或可压缩性,建立稀疏采样图像重构问题的优化模型。然后,构造适当的随机稀疏采样模板,对目标图像的傅里叶分量进行采样测量。最后,利用随机稀疏测量样本,通过非线性优化精确重构目标图像。实验结果显示,对实际的卫星图像,利用20%～30%随机测量样本非线性重构图像与利用全部测量样本直接重构图像的均方误差仅为4%～6%,表明利用随机稀疏傅里叶样本能够实现精确的图像重构,而且大大减少了测量样本的数量,从而有效降低了实现快速成像对傅里叶望远镜系统的成本和复杂性要求。In order to realize rapid imaging of Fourier telescopy, an approach of image reconstrucuon via sparse sampling is proposed and the accurate image reconstruction by using sparse Fourier samples is investigated. Firstly, based on compressed sensing theory and the sparsity or compressiveness of object images in transformation domains, the optimization model of image reconstruction via sparse sampling is established. Then, appropriate masks for random and sparse sampling are constructed to sample Fourier components of object images. Finally, object images are reconstructed accurately through nonlinear optimization by using the random and sparse samples. Experimental results indicate that the RMS errors of reconstructed images between 20%-30 % sampling and full Sampling are only 4%-6 %, which shows that the proposed approach can realize accurate image reconstruction by using random and sparse Fourier samples and can reduce the amount of measurement samples greatly. The method lowers the requirements of costs and complexity to Fourier telescopy systems for rapid imaging effectively.

关 键 词：傅里叶望远镜 稀疏采样 压缩感知 非线性优化 

分 类 号：P111.5[天文地球—天文学] TP391[自动化与计算机技术—计算机应用技术]