Reversible n-bit to n-bit integer Haar-like transforms

Methods of producing reversible n-bit to n-bit integer transforms is presented in this paper. Such methods are particularly suited for hardware-based implementations, as keeping the coefficients to n bits simplifies the design of custom hardware and makes it easier to use these approaches on preexisting hardware with limited channel width. One of our methods, called table-lookup Haar (TLHaar) is an approximation of the Haar integer wavelet transform (Haar IWT). The Haar IWT takes two integer data values A and B and using averaging and differencing produces a low-pass value L and a high-pass value H, both integers. The lookup tables are created by initializing each with an identity transform. TLHaar executes up to 44% faster. Compression results are mixed, and depend on the compression method used and the image type.