Matrix transformation of digital image and its periodicity

摘要

The periodicity of a general matrix modular transformation is discussed, and a simple proof of a sufficient and necessary condition that a matrix transformation has periodicity is given. Using a block matrix method, the higher dimensional transformation and its inverse are studied, and a simple algorithm for calculating their periods is put forward. The security of n-dimensional Amold transformation and its inverse is also discussed. The results show that the two transformations are applicable in scrambling and recovering images.