基于超稀疏结构学习的压缩感知重建研究

项目名称： 基于超稀疏结构学习的压缩感知重建研究

项目编号： No.61302190

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 武娇

作者单位： 中国计量学院

项目金额： 25万元

中文摘要： 设计面向复杂图像的压缩感知(Compressive sensing，CS)重构算法是将CS理论成功应用于解决实际工程中的图像处理等问题的重要环节。本项目针对不同框架下的CS重构问题中图像先验结构信息的挖掘和建模、自适应结构模型学习、以及结构信息的有效利用等关键问题展开研究。在结构化CS框架下，建立图像的结构先验正则模型，并设计基于学习的结构先验正则和自适应结构字典的CS图像重构算法。在统计压缩感知框架下，建立基于Gaussian模型的结构稀疏模型，利用Bayesian学习和结构先验正则学习方法设计快速有效的CS图像重构算法。在核压缩感知框架下，构建信号在特征空间中的结构稀疏模型和重构算法，分析特征空间中结构模型对重构性能的影响，验证模型和算法的有效性与先进性，并对统计压缩感知重构与核压缩感知重构之间的联系进行理论研究。本项目对将CS理论进一步推广到时间连续信号的情况具有重要的理论价值。

中文关键词： 压缩感知；图像重构；统计模型；结构模型；字典学习

英文摘要： Designing compressive sensing (CS) image reconstruction algorithms is an important link of successfully applying theory in practice. This project focuses on the key techniques of CS reconstruction based on the varying frameworks in exploring and modeling the structure prior information of images, learning the structured models adaptively, and making full use of the structure knowledge. Under the structured CS framework, the structured prior regularization models will be designed, and the CS image reconstruction algorithms based on the adaptive structured regularization and structured dictionary learning will be developed. Under the statistics CS framework, the structued sparse models based on Gaussian models will designed, and the fast and effective sparse estimation algorithms will be proposed by using Bayesian learning and structure prior regularization learning. Under kernal CS framework, the structured sparse models and reconstruction algorithms in featrue space will be designed. Their effectiveness and novelties will be validated. In addition, the relationship between statistical CS reconstruction and kernel CS reconstruction will be studied further.The researches of this project have important theoretical value for furhter extending CS theory to the case of time continuous signals.

英文关键词： compressive sensing；image reconstruction；statistical model；structured model；dictionary learning