Abstract: Focused on the high computational complexity and long encoding time problems in the traditional fractal image compression, an orthogonalized fractal encoding algorithm based on texture features of gray-level co-occurrence matrix was proposed. Firstly, from the perspective of feature extraction and image retrieval, the similarity measurement matrix between range blocks and domain blocks was established to transform the global search into the local search, so as to reduce the codebook. Then, by defining a new normalized block as the new gray-level description feature, the transformation process between blocks was simplified. Finally, the concept of Simultaneous Orthogonal Matching Pursuit (SOMP) sparse decomposition orthogonalized fractal encoding was introduced, so that the gray-level matching between blocks was transformed into solving the corresponding sparse coefficient matrix, which realized the matching relationship between one range block and multiple domain blocks. Experimental results show that compared with Sparse Fractal Image Compression (SFIC) algorithm, the proposed algorithm can save about 88% of the encoding time on average without reducing the quality of image reconstruction; compared with the sum of double cross eigenvalues algorithm, the proposed algorithm can significantly shorten coding time while maintaining better reconstruction quality.

Key words: fractal image compression, gray-level co-occurrence matrix, similarity measurement, gray matching, sparse coefficient, Simultaneous Orthogonal Matching Pursuit (SOMP)

摘要： 针对传统分形图像压缩中存在计算复杂度高以及编码时间较长的问题，提出了一种基于灰度共生矩阵纹理特征的正交化分形编码算法。首先，从特征提取和图像检索的角度建立起范围块和域块之间的相似性度量矩阵，由此将全局搜索转化为局域搜索来缩减码本；然后，定义一个新的规范块作为新的灰度描述特征，从而简化了块之间的变换过程；最后，引入同步正交匹配追踪（SOMP）稀疏分解正交化分形编码的概念，将块之间的灰度匹配转化为求解相应的稀疏系数矩阵，进而实现了一个范围块和多个域块之间的匹配关系。实验结果表明，与稀疏分形图像压缩（SFIC）算法相比，所提算法在不降低图像重建质量的前提下节省平均约88%的编码时间；与双交叉和特征算法相比，所提算法能够在保持更好的图像重建质量的同时显著缩短编码时间。

关键词: 分形图像压缩, 灰度共生矩阵, 相似性度量, 灰度匹配, 稀疏系数, 同步正交匹配追踪