Design Schemes of Linear-Phase LOT Using Groups of Rotation and Permutation in Multi-Dimensional Orthogonal Space

Abstract

In this paper, a new design scheme of multi-dimensional linear-phase lapped orthogonal transform (LOT) for image and audio coding is proposed. For even N, LOT basis functions described by (N × 2N) matrix, can be generated by rotation and permutation of Nth-order normalized orthogonal vectors in 2N-dimensional orthogonal space. These operations generate rotation groups and permutation groups and by using properties of these groups, the number of parameters which optimize coding gain can be reduced effectively. Furthermore several design examples of LOT are given to validate the proposed scheme.