Optimization of AIQ representations for low complexity wavelet transforms

The Discrete wavelet transform (DWT) has been used in a wide range of real-time application. Algebraic integer quantization (AIQ) encoding has been proposed to represent the irrational transform basis of the wavelet transform as polynomials with integer coefficients. In this paper, we suggest to restate these polynomials to obtain simpler coefficients for both the integer coefficients and the polynomial basis, while keeping numerically equivalence with the original AIQ coefficient. We present an integer linear programming (ILP) model for restating these linear expressions. The results show that for the considered DAUB66 wavelet, the number of additions required can be reduced by up to 18% compared to earlier work.