基于先验信息的稀疏信号重构理论与算法研究

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1、目录i目目目录录录目录······································································i摘要······································································iiiAbstract·································································v1绪论······························

2、·····································11.1研究背景及意义···················································11.2研究现状··························································21.3本文主要工作及全文组织结构······································42压缩感知基本理论··································

3、···················52.1信号的稀疏表示···················································52.2测量矩阵的设计···················································62.3信号的重构算法···················································72.4本章小结···················································

4、·······83基于先验信息下的l1−l1和l1−l2范数极小化问题研究···················93.1基于先验信息的l1−l1极小化重构理论······························93.2基于先验信息的l1−l2极小化重构理论······························103.3数值实验··························································113.4本章小结··························

5、································124PI-IRLS算法对稀疏信号的重构问题研究······························154.1基于先验信息下的无约束lq范数极小化重构理论·····················154.2PI-IRLS算法和基本定义···········································164.3PI-IRLS算法的理论分析···········································174.4数

6、值实验··························································264.5本章小结··························································29ii西南大学硕士学位论文5总结与展望····························································315.1本文工作的总结············································

7、·······315.2未来工作的展望···················································31参考文献·································································33致谢······································································39已完成文章目录········································

8、···················41目录摘要基于先验信息的稀疏信号重构理论与算法研究统计学专业硕士研究生冯念慈指导教师王建军教授摘要随着信息时代的到来,数据正逐渐应用到许多领域中.面对每天成倍增加的数据,如何对它进行存储、采集和运输,一直都是学术界关注的热点.作为一种能有效处理高维数据的新颖理论,