Reversible component transforms by the LU factorization

A scaled transform is defined for a given irreversible linear transformation based on the LU factorization of a nonsingular matrix so that the transformation may be computed in a lifting form and hence may be reversible. Round-off errors in the lifting computation and the computational complexity are analyzed. Some reversible component transforms are presented and experimented to give some remarks to image compression applications. Discussions are developed with coding gain and actual bit rates.