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数论变换算法的拓展与在图像压缩中应用

he Extending of Number Theoretic Transform and Applications in Image Compression

中文摘要英文摘要

本文研究并利用了数论变换的性质、特点以及快速算法的优势,结合图象数据的特点以及二维序列与变换系数之间的关系,拓展了数论变换算法,提出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并给予证明。使用CCITT推荐的8幅二值图像进行验证和分析,结果表明,数论变换快速算法及提出的两个定理,用于对图像数据的压缩是可行的,且分块适当可提高运算速度,减少存储空间,提高压缩比。本文算法在图象压缩中应用具有较大的理论意义和应用价值,为数论变换在图像压缩中的应用迈出了实际应用的第一步。

his paper studies and uses the property, characteristics and advantages of fast algorithm of NTT(Number Theoretic Transform), combines with the characteristics of image data and the relationship between NTT coefficients and 2-D sequence in order to extend NTT algorithm, and proposes transpose algorithm on 2-D NTT and the theorem on the relationship between NTT coefficients and periodic 2-D data which are proved by this paper. We use eight bit-level images recommended by CCITT for certification and analysis, and the experimental results show that the fast algorithm of NTT and the two presented theorem can 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 images compression.

刘兵、张虹

数学计算技术、计算机技术

数论变换整型变换图像压缩快速算法

Number Theoretic TransformInteger transformimage compressionFermat number transformfast algorithm

刘兵,张虹.数论变换算法的拓展与在图像压缩中应用[EB/OL].(2006-06-19)[2025-08-25].http://www.paper.edu.cn/releasepaper/content/200606-320.点此复制

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