Scaled Lifting Scheme and Generalized Reversible Integer Transform

In this paper, we generalize the lifting scheme and the triangular matrix scheme. For the existing lifting scheme and the triangular matrix scheme, the entries on the diagonal line must be 1 or 2^k. In this paper, we find that this constraint can be relaxed and the lifting or the triangular matrix is still reversible. Thus, the constraint that det(A) = 2^L is not required and we can convert a matrix into a reversible integer transform without pre-scaling even when det(A) ne 2^L. Moreover, the proposed scaled schemes are also helpful for improving the accuracy and reducing the implementation complexity.