双层非负矩阵分解的分形图像压缩算法

doi:10.3778/j.issn.1002-8331.2009-0350

摘要/Abstract

摘要： 分形图像压缩作为一种基于结构的图像压缩技术，在许多图像处理中得到了应用。但是分形图像压缩的编码阶段非常耗时，且重建图像的质量效果不佳。针对这些问题，提出了一种基于双层非负矩阵分解的分形图像压缩编码算法。在传统的非负矩阵分解理论上，将投影非负矩阵分解与[L3/2]范数约束相结合，可以在较短的时间内提取具有代表性的图像特征。算法采用双层非负矩阵分解提取原始图像的特征，对图像的特征进行[K]均值聚类，根据对应索引得到分类的图像块，在相应类别块里进行正交稀疏分解得到分形码，最后重建图像。实验结果表明，与快速稀疏分形图像压缩理论重建的图像相比，双层非负矩阵分解的分形压缩算法提高了重建图像的质量，同时缩短了编码时间。

关键词: 非负矩阵分解, 投影非负矩阵分解, 正交匹配追踪, [K]均值聚类, 稀疏分形图像压缩

Abstract: As a structure-based image compression technology, fractal image compression is used in many image processing. However, the encoding stage of fractal image compression is very time-consuming, and the quality of the reconstructed image is not good. To solve these problems, a fractal image compression coding algorithm based on double-layer non-negative matrix factorization（DLNMF） is proposed. In the traditional theory of non-negative matrix factorization（NMF）, the projection non-negative matrix factorization（PNMF） is combined with the [L3/2] norm constraint to extract representative image features in a short time. Firstly, the features of the original image are extracted by double-layer non-negative matrix decomposition; then the image features are clustered by [K]-means, and the classified image blocks are obtained according to the corresponding index; orthogonal sparse decomposition is performed in the corresponding class blocks to obtain the fractal code; and finally, the reconstructed image is obtained according to the fractal code. Experimental results show that compared with images reconstructed by fast sparse fractal image compression theory, the fractal compression algorithm of double-layer non-negative matrix factorization improves the quality of the reconstructed image and shortens the encoding time.

Key words: non-negative matrix factorization, projected non-negative matrix factorization, orthogonal matching pursuit, [K]-means clustering, sparse fractal image compression

方美东, 王辉, 张爱华. 双层非负矩阵分解的分形图像压缩算法[J]. 计算机工程与应用, 2022, 58(8): 204-213.

FANG Meidong, WANG Hui, ZHANG Aihua. Fractal Image Compression Algorithm Based on Double-Layer Non-Negative Matrix Factorization[J]. Computer Engineering and Applications, 2022, 58(8): 204-213.

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