基于张量字典学习的压缩感知视频重构

吴育新 陈利民 杨雄辉

摘  要： 传统的基于矩阵形式的视频图像重构算法，由于其二维表达矩阵的局限性，在重构过程中降低了相邻帧图像之间的关联性以及图像的重构质量。为了克服该问题，提出一种基于张量字典学习的压缩感知视频重构算法。把视频图像的二维空间特性和一维时间特性映射到三阶张量上，保持了图像的时间特性，增强了图像前后帧之间的相关性。同时在重构视频图像块的过程中，相对于二维矩阵字典，原子的稀疏表达有着更高的自由度，进而提高了重构质量。对张量的计算在傅里叶域中进行，减少了算术运算的次数，缩短了重构时间。通过实验数据以及视觉直观证明，提出的算法重构图像的峰值信噪比较传统方法提高了2～4 dB。

关键词： 压缩感知; 视频图像重构; 张量分解; 稀疏表达; 傅里叶域; 张量计算

中图分类号： TN911.73?34                         文献标识码： A                       文章编号： 1004?373X（2020）03?0066?04

Compressed sensing video reconstruction based on tensor dictionary learning

WU Yuxin， CHEN Limin， YANG Xionghui

（Information Engineering School of Nanchang University， Nanchang 330000， China）

Abstract： In the conventional matrix?based video image reconstruction algorithm， the correlation between adjacent frame images and the quality of image reconstruction are reduced due to the limitation of two?dimensional representation matrix. In view of the above， a compressed sensing video reconstruction algorithm based on tensor dictionary learning is proposed. The two?dimensional spatial and one?dimensional temporal characteristics of a video image are mapped to a third?order tensor， which preserves the temporal characteristics of the image and enhances the correlation between the two adjacent frames. Meanwhile， in the process of reconstructing video image blocks， the sparse representation of atoms has a higher degree of freedom relative to the two?dimensional matrix dictionary， which thus improves the reconstruction quality. The calculation of tensor is performed in Fourier domain， which reduces the number of times of arithmetic operation and shortens the reconstruction duration. The experimental data and visual evidence show that the proposed algorithm can increase the PSNR （peak signal?to?noise ratio） of reconstructed images by 2～4 dB， compared with conventional algorithms.

Keywords： compressed sensing; video image reconstruction; tensor decomposition; sparse representation; Fourier domain; tensor calculation