第18卷第3期 2010年3月
1004-924X(2010)03-0521-07
文章编号
光学精密工程
Optics and Precision Engineering
稀疏采样傅里叶望远镜成像
刘欣悦，董磊，王建立
（中国科学院长春光学精密机械与物理研究所，吉林长春130033）
Vol.18No.3 Mar.2010
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间题进行了研究。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间题的优化模型。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，
调：里叶望远镜释疏来样；压缩感知；非线性优化
关键
中图分类号：P111.5;TP391
文献标识码：A
Fouriertelescopyimagingviasparsesampling
LIU Xin-yue, DONG Lei, WANG Jian-li
(Changchun Instituteof Optics，FineMechanics andPhysics， ChineseAcademyofSciences，Changchun130033，China)
Abstract: In order to realize rapid imaging of Fourier telescopy, an approach of image reconstruction 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 ima-ging effectively.
Key words: Fourier telescopy; sparse sampling; compressed sensing; nonlinear optimization
收稿日期：2009-05-06；修订日期：2009-07-27
基金项目：国家863高技术研究发展计划资助项目（No.2008AA7034250）