On implementing transforms from integers to integers

Arbitrary linear transforms are often applied to integer valued data sequences, producing non-integer outputs. In such cases, it is often desirable to approximate the true transform with a non-linear transform producing integer outputs as close as possible to the true transform, while retaining the reversibility property of a transform. This paper proposes a new approach to implement transforms that map integers to integers in a reversible way. The approach aims to develop a reversible implementation that minimizes the average distortion between the integer outputs and the outputs of the true linear transform