线性变换SERM分解选取的快速方法

Fast Selection Method for SERM Factorizations of Linear Transforms

给出了一种线性变换的整数SERM分解的选取方法。通过大量的实验 ,发现SERM分解的近似最优结果是大量存在的 ,而且这些近似最优结果的分布是分散的 ,当分解结果的误差度量比较小时的时候 ,有当置换矩阵相近时 ,分解结果的误差也相近的实验事实。基于此观察结果 ,给出了基于局部搜索的SERM分解的近似最优分解方法 ,可以得到非常接近最优分解的结果。此方法的收敛速度很快 ,只需很少的几次搜索即可得到可以实用的结果 ,同时我们利用所选取的分解结果做了无失真图像压缩的实验 ,并得到了不错的结果。

A selection method of SERM factorizations for linear transforms is presented.It is discovered that the near optimal results are almost everywhere and when the factorization error is small,the closer the permutation matrices,the closer the results.According this fact,A local search is proposed that based near optimal factorization method which can obtain the near optimal results.Moreover,this method convergence very fast,can usually obtain useful results by very limited iterations.It is tested lossless image coding with the selection results and good results is obtained.