A Fast Two-Dimensional Karhunen-Loeve Transform
Robert M. Haralick, Norman C. Griswold, Nimitra Kattiyakulwanich · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1975
One frequently used image compression method is based on transform coding. In terms of RMS error, the best transform is the Karhunen-Loeve (Principal Components). This method is not generally used due to computational complexity. In this paper we show that under isotropicity conditions the Karhunen-Loeve is almost separable and that an approximate fast principal components transform exists. Our results indicate that the fast K-L is nearly as good as the true K-L and that it yields better results than other discrete transforms such as DLB, SLANT, or Hadamard. The approximations and errors are discussed in terms of the RMS and RMS correlated error.