Error-Free Arithmetic for Discrete Wavelet Transforms Using Algebraic Integers

In this paper a novel encoding scheme is introduced with applications to error-free computation of Discrete Wavelet Transforms (DWT) based on Daubechies wavelets. The encoding scheme is based on an algebraic integer decomposition of the wavelet coefficients. This work is a continuation of our research into error-free computation of DCTs and IDCTs, and this extension is timely since the DWT is part of the new standard for JPEG2000. This encoding technique eliminates the requirements to approximate the transformation matrix elements by obtaining their exact representations. As a result, we achieve error-free calculations up to the final reconstruction step where we are free to choose an approximate substitution precision based on a hardware/accuracy trade-off.