吳育新 陳利民 楊雄輝

摘? 要： 傳統(tǒng)的基于矩陣形式的視頻圖像重構(gòu)算法，由于其二維表達(dá)矩陣的局限性，在重構(gòu)過程中降低了相鄰幀圖像之間的關(guān)聯(lián)性以及圖像的重構(gòu)質(zhì)量。為了克服該問題，提出一種基于張量字典學(xué)習(xí)的壓縮感知視頻重構(gòu)算法。把視頻圖像的二維空間特性和一維時(shí)間特性映射到三階張量上，保持了圖像的時(shí)間特性，增強(qiáng)了圖像前后幀之間的相關(guān)性。同時(shí)在重構(gòu)視頻圖像塊的過程中，相對于二維矩陣字典，原子的稀疏表達(dá)有著更高的自由度，進(jìn)而提高了重構(gòu)質(zhì)量。對張量的計(jì)算在傅里葉域中進(jìn)行，減少了算術(shù)運(yùn)算的次數(shù)，縮短了重構(gòu)時(shí)間。通過實(shí)驗(yàn)數(shù)據(jù)以及視覺直觀證明，提出的算法重構(gòu)圖像的峰值信噪比較傳統(tǒng)方法提高了2～4 dB。

關(guān)鍵詞： 壓縮感知; 視頻圖像重構(gòu); 張量分解; 稀疏表達(dá); 傅里葉域; 張量計(jì)算

中圖分類號： TN911.73?34? ? ? ? ? ? ? ? ? ? ? ? ?文獻(xiàn)標(biāo)識碼： A? ? ? ? ? ? ? ? ? ? ? ?文章編號： 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