周四望+刘龙康

摘 要：稀疏性是压缩感知的前提，然而，自然图像通常不是稀疏的，因此对图像直接应用压缩感知算法很难取得高压缩效率.针对图像信号，将编码思想融入压缩感知理论，提出一种简单有效的零树压缩感知方法.该方法先利用零树思想辅助压缩感知测量，在得到测量值的同时编码重要系数的位置；然后提出零树追踪重构算法，通过精确解码重要系数位置来重构原始图像小波系数，提高重构精度.实验结果表明，相比于现有匹配追踪算法和EZW算法，本文方法有更高的压缩比和更好的图像重构质量.

关键词：小波变换；图像处理；压缩感知；编码

中图分类号：TP37 文献标志码：A

Image Zerotree Compressed Sensing

Based on Wavelet Transform

ZHOU Siwang，LIU Longkang

（College of Information Science and Engineering，Hunan University， Changsha 410082，China）

Abstract：The basic principle of Compressed Sensing （CS） theory is that if a signal is sparse， CS promises to deliver a full recovery of this signal with high probability from far fewer measurements than the original signal. Unfortunately， image signals usually are not sparse， and thus it is difficult to obtain high compression performance for image compressed sensing.This paper proposed a simple and efficient zerotree compressed sensing method for images. In the proposed scheme， the classical zerotree coding is integrated into the process of measure to encode the precise locations of significant elements， which is used to restore the original image by the proposed pursuit reconstruction algorithm to improve the quality of the reconstructed image. The experimental results show that， compared with the existing matching pursuit algorithms and Embedded Zerotree Wavelet （EZW） coding algorithm， the proposed algorithm achieves much higher compression ratio and better image quality.

Key words：wavelet transform；image processing； compressed sensing； encoding

小波变换是图像压缩的重要方法[1].当图像信号经由小波变换转换到小波域后，其小波域系数隐含多分辨的树结构，存在相关性.在图像的小波域系数中，如果父系数小于给定的阈值，则其子系数也很大概率小于此阈值，利用此相关性对小波系数做进一步的编码，可显著增加图像压缩性能.嵌入式小波零树编码（EZW）[2]是最经典的一种图像编码方法，通过设计正重要系数、负重要系数、孤立零和零树根，将小于阈值的父子小波系数组织成树结构，提高了图像压缩比.

Donoho等[3-5]认为，上述传统变换压缩方法鲁棒性差，而且压缩效率存在“自适应”的特点并且依赖信号本身的结构，进而提出了一种称为“压缩感知”的新理论，近年来吸引了越来越多研究人员的关注……