NTT--数论变换算法在图像压缩技术中的应用研究

提出了一种全新的图像数据压缩算法，即数论变换（Ｎｕｍｂｅｒ Ｔｈｅｏｒｙ Ｔｒａｎｓｆｏｒｍａｔｉｏｎ，ＮＴＴ）算法，证明了在以正整数ｐ为模的整数环Ｚｐ上ＮＴＴ是线性正交变换，以及在Ｚｐ上具有卷积特性等，设计了具有ＦＦＴ类型的快速算法，该算法可采用移位操作实现，其程度优于ＤＣＴ变换，最后通过实例比较，说明了该算法在图像数据压缩中表现出运算速度快、精度高和压缩效果好等优点，ＮＴＴ算法的研究，为图像压

The Research on Arithmetic of the Number Theory Transformation Applied in the Image Compression

This paper puts forward a new image compression arithmetic, the Number Theoretic Transformation (NTT). It proved that the NTT on the integral ring Z\-p module p is linear transformation and the NTT on Z\-p has the convolution characteristic, and a quick arithmetic with FFT is designed. The arithmetic may be realized by shift and its velocity is superior to the DCT transformation. Finally by contrast of instances, it is indicated that this method represents such advantages as fast velocity, high precision, and good effect of compression, etc.. The study on NTT arithmetic exploits a new way for the image compression technique.