基于数学形态学的二值文字水印信息稀疏表征方法

水印信息的最佳稀疏域是基于压缩感知理论的矢量数据水印算法研究的基础，也是解决小数据量矢量数据水印嵌入的关键所在. 本文提出了一种基于数学形态学的二值文字水印信息稀疏表征方法，分析了二值文字水印信息的特征，提出了基于数学形态学的水印信息稀疏表征方法，将原始的水印信息有效地进行了稀疏表达，并对提出的稀疏表达方法进行了实验验证. 结果表明，该方法能够较好地对二值文字水印信息进行稀疏表达，有效提高了水印信息的压缩比，可以去除无关水印判读的冗余信息，为满足基于压缩感知理论水印算法的研究提供了好的理论基础.

The Sparse Method of Binary Text Watermark Information Based on Mathematical Morphology

The optimized sparse domain of watermarking information is the foundation of studying watermarking algorithm for vector geographic data based on compression sensing theory，and it is also the key to solve the challenge to embed the watermarks into small data. A sparse representation based on mathematical ecology is proposed for binary-character watermarking information. Firstly，the features of the binary-character watermarking information are analyzed. Then，the spare representation based on mathematical ecology is proposed，and it is used for the original watermarking information. Finally，the experimental verification is given for the proposed sparse representation. The results show that the method can embed the binary-character watermarking information in a sparse way，increase the compression ratio for watermarking information effectively，and remove the redundant information unrelated with identification of watermarking. Therefore，the proposed method provides a good theoretical foundation for research of watermarking algorithm based on compression sensing theory.