基于Tetrolet Packet变换的SAR图像稀疏表示

摘要

Tetrolet变换作为多尺度几何分析的一种,能够对平滑的自然图像进行有效的稀疏表示.SAR图像具有丰富的细节纹理信息,因此经过Tetrolet变换后的高频系数依然具有较大的幅值,从而严重影响了稀疏表示SAR图像的性能.该文针对此问题提出了一种新的变换方法Tetrolet Packet,该算法将高频子带系数进行重新排序后,使用熵作为代价函数对不同的高频子带进行不同层次的Tetrolet分解得到Tetrolet最优分解树,从而使系数能量更加集中同时尽量减少方向信息,以便于后续SAR图像压缩.实验比较了Tetrolet和TetroletPacket两种算法,用相同个数的变换系数来进行图像重建,无论是主观视觉质量还是客观参数PSNR评价,Tetrolet Packet稀疏表示SAR图像的性能都优于Tetrolet.最后针对两种算法的变换系数均具有类似零树结构的特性,提出分别使用SPIHT和Modified-SPIHT算法对Tetrolet和Tetrolet Packet变换系数进行编码,并探讨了该两种算法对SAR图像的压缩性能.%Tetrolet transform, as one of the mutiscale geometric analysis method, can be used to represent natural images sparsely. However, SAR images consist of textures, leading to that the high frequency coefficients of Tetrolet still have large amplitude, and thus affects the sparse representation performance of SAR images seriously. In this paper, a new transform named Tetrolet Packet is proposed. At first, the high frequency coefficients are reordered, and then the high frequency sub-bands are decomposed using multi-Tetrolet transform according to a entropy based cost function. So a optimal Tetrolet tree structure can be found, and the energy of coefficients are concentrated with less direction informations in order to get better performance of SAR image compression. In the experiment, the SAR images are reconstructed with the same number of coefficients of Tetrolet transform and Tetrolet Packet respectively, and their reconstruction performances are compared. The results show that the proposed method Tetrolet Packet outperforms Tetrolet in the sense of sparse representation ability for SAR images, both in visual quality and PSNR. Furthermore, transform coefficients of both methods have similar zero-tree structures, and the compression performance of the proposed method is investigated by employing Modified-SPIHT.