Integer sinusoidal transforms for image processing

The sine and cosine transforms, which are popular transforms for image coding, are members of a sinusoidal transform family. Each member of the family is the optimal KLT of a Markov process. This paper derives the conditions under which the order-8 sinusoidal transforms can be approximated by orthogonal integer transforms which can be implemented using integer arithmetic. Some integer transforms are derived as examples. The results show that for the popular even sine-1, even sine-2 and the cosine transforms, there is an infinite number of integer transforms and some have their transform component magnitudes less than eight. In LSI implementation, if low implementation cost and fast computation speed are paramount, then an integer transform of small component magnitudes can be chosen. If better performance is desired, integer transforms whose elements have larger magnitudes can be used. The availability of many integer transforms provides a design engineer the freedom to trade-off performance against simple implementation and speed.