数论变换与周期性序列关系在图像压缩中应用

Applications of Relationship Between Number Theoretic Transform Coefficients and Periodic Sequence in Image Compression

利用数论变换的性质、整型变换的特点、变换速度快和算法简单的优势,结合图像数据的特点以及二维序列与变换系数之间的关系,提出并证明了数论变换转置定理和周期性二维序列与变换系数关系定理.该定理为用于二值图像压缩奠定了理论基础,特别是利用周期性二维序列与变换系数间的关系来判断图像是否具有周期性,进而确定其行列周期,以达到提高压缩比的目的.使用国际电报电话咨询委员会(CCITT)推荐的8幅二值图像进行验证,结果表明:数论变换快速算法及证明的两个定理,用于对图像数据的压缩是可行的,若分块适当可提高运算速度,减少存储空间,提高压缩比.提出的算法在图像压缩中应用具有较大的理论意义和应用价值.

For making use of the property of NTT （Number Theoretic Transform） well, which is integer, fast and simple, combining with the characteristics of image data and the relationship between NTT coefficients and 2-D sequence, the transpose algorithm on 2-D NTT and the theorem on the relationship between NTT coefficients and periodic 2-D data were proposed. The above theorem establish the theory foundation for NTT while using in image compression, especially for utilizing the relationship between NTT coefficients and periodic 2-D data to judge periodicity of images. Based on that, this periods of rows can be confirmed, the compression rate can be improved too. We use eight bit-level images recommended by CCITT for certification, and the experimental results show that the fast algorithm of NTT and the two presented theorem can be used in image compression, and if the block size is proper, they can improve processing speed, reduce storage space and improve the compression ratio. The algorithms proposed in this paper have biggish theoretical and practical value, and take the first step for NTT algorithm in the application of image compression.