摘要压缩感知是由D. Donoho和E. Candes等在2006年提出的，是一种基于信号稀疏性可同时实现采样和压缩的信号处理理论。压缩感知具有减少采样时间、降低采样设备要求的特点，其应用研究涉及许多领域，如：雷达成像技术、人脸识别、MRI、遥感图像处理等。压缩感知理论作为一种新型的信号获取方式，在视频图像获取问题中的应用具有重要的理论意义和实用价值。视频序列中相邻图像所表示的内容变化不大，图像间具有很强的相关性。因此，视频图像所含信息是高度冗余的，如何体现并利用这种相关性将对视频序列的重建效果有着重要的影响。本文对现有两种典型的视频图像压缩感知重建算法进行总结和分析，在此基础上，提出了一种新的基于帧间相关性的视频图像压缩感知重建算法，并且应用Matlab语言编程，获得算法的实现。与现有两种算法相比，本文改进算法的重建结果在PSNR及SSIM上有不同程度的提高。63920

毕业论文关键词  压缩感知；帧间相关性；视频序列；图像重建；

毕业设计说明书（论文）外文摘要

Title  The inter-frame correlation based compressed sensing video reconstruction method                        

Abstract Compressed sensing was proposed by D. Donoho and E. Candes in 2006. This theory relies on the fact that most of the natural signals can be sparsely represented in some transform domain. Compressed sensing can lead to reduced sampling time and simpler requirement for equipment. It has been applied in many fields, such as radar imaging technology, face recognition, MRI, and remote sensing image processing. As a new signal acquisition method, compressed sensing theory has an important theoretical significance and practical value in the application of the video image acquisition problem. Due to the little difference, the adjacent video images have strong correlation with each other. Therefore, the information contained in the video image is highly redundant. How to reflect and take advantage of the correlation has an important impact on the reconstruction of video sequences. In this paper, existing two typical compressed sensing reconstruction algorithms for video are concluded and analyzed. At last, a new inter-frame correlation based video reconstruction algorithm is proposed and the Matlab programming language is used to implement the new algorithm. Compared with the two existing algorithms, the proposed algorithm has a certain effect on the increase of PSNR and SSIM of reconstructed images.

Keywords  Compressed sensing  Inter-frame correlation  Video sequence       Image reconstruction

1   引言 1

1．1  研究背景和意义 1

1. 2  压缩感知理论简介 2

1.2.1  信号的稀疏表示 2

1.2.2  压缩感知线性测量 3

1.2.3  压缩感知非线性重建 3

2   二维图像压缩感知测量与重建 4

2. 1  传统的二维图像压缩感知测量与重建方法 4

2.1.1  传统的二维图像压缩感知测量过程 4

2.1.2  传统的二维图像压缩感知重建过程 5

2. 2  基于块的二维图像压缩感知测量与重建方法(BCS-SPL) 5

2.2.1  基于块的二维图像压缩感知测量过程 5