Improved reversible integer transform

Integer transform are the discrete transforms whose entries are summations of 2^-k. If for an integer transform, we can perfectly recover the input from the output, we call it the reversible integer transform. In 2001, Hao and Shi developed an algorithm that can convert any reversible non-integer transform into a reversible integer transform. In this paper, we improve their works. First, we simplify the way of derivation. Then, we analyze the approximation error and introduce the way to reduce it. We also discuss the problem of bit constraint and how to reduce the number of time cycle in implementation