基于Tetrolet变换的图像稀疏逼近算法

摘要

针对现有大部分图像稀疏逼近算法通用性不强,仅对具有某类特征的图像具有最优逼近性能的问题,利用小波变换与Tetrolet变换各自的优点,提出了一种通用性强,不受图像特征限制的图像稀疏逼近算法.该算法分别利用小波变换与Tetrolet变换对图像的平滑区域与细节区域进行稀疏逼近,先提取平滑区域,对平滑区域进行修正,然后对修正后的平滑区域进行稀疏逼近.根据平滑区域稀疏逼近的结果分离出细节区域,实现对细节区域的稀疏逼近.对一系列典型图像进行仿真的结果表明,该算法通用性强,不受图像特征的限制,在同等条件下,图像重构质量比传统小波变换高约5.5 dB,比Tetrolet变换高约1.0 dB.%Since most of image sparse approximation algorithms are not universal, and these algorithms could achieve optimal approximation at the special image with certain detail, a new algorithm based on the advantages of wavelet and tetrolet transform is proposed. The new algorithm exploits the advantages of the wavelet transform for the representation of smooth images and the ability of the tetrolet transform to represent details. Firstly, the smooth region are extracted and amended, then the smooth region is sparsely represented. Finally, the detail region based on the representation of smooth images is extracted, and the sparse representation of the detail region is implemented. The results of experiment show that the new algorithm is universal and it does not depend on the image detail. The image construction in quality is better than the wavelet transform by about 5. 5 Db and the Tetrolet transform by about 1. 0 Db at the same conditions.