基于亚高斯随机投影的图像重建方法  

A Method of Image Reconstruction Based on Sub-Gaussian Random Projection

作　　者：方红[1] 章权兵[1] 韦穗[1] 

机构地区：[1]安徽大学计算智能与信号处理教育部重点实验室

出　　处：《计算机研究与发展》2008年第8期1402-1407,共6页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60603083,60473102);高等学校博士学科点专项科研基金项目(20070357003)~~

摘　　要：将亚高斯随机投影引入可压缩传感CS(compressed sensing)理论,给出了两种新类型的CS测量矩阵:稀疏投影矩阵和非常稀疏投影矩阵.利用亚高斯分布尾部的有界性,证明了这两种矩阵满足CS测量矩阵的必要条件.同时,进一步说明由于这两种矩阵构成元素的稀疏性可以简化图像重建过程中的投影计算,从而提高重建速度.实验结果表明新的测量矩阵均有较好的测量效果,在满足一定测量数目要求的条件下可以精确重建.最后给出了这两种矩阵与一般采用的高斯测量矩阵的重建结果比较和分析.In this paper, sub-Gaussian random projection is introduced into compressed sensing （CS） theory and two new kinds of CS measurement matrix, sparse projection matrix and very sparse projection matrix are presented. By the tail bounds for sub-Gaussian random projections, the proof of how these new matrices satisfy the necessary condition for CS measurement matrix is provided. Then, it is expatiated that owing to their sparseness, new kinds of matrices greatly simplify the projection operation during image reconstruction, which simultaneously greatly improves the speed of reconstruction. Further, it can be easily proved that Gaussian matrix and Bernoulli matrix are special matrices obeying sub-Gaussian random distribution, which indicates that new measurement matrices extend the current results on CS measurement matrix. Both the results of simulated and real experiments show that with a certain number of measurements, new matrices have good measurement effect and can acquire exact reconstruction. Finally, the comparison and analysis of reconstruction results respectively adopting new matrices and Gaussian measurement matrix is conducted. Compared with Gaussian measurement matrix, new matrices have lesser average over-sampling factor, which indicates lower complexity of reconstruction.

关 键 词：亚高斯 随机投影 可压缩 稀疏性 测量矩阵 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]