Fast Algorithm for Constructing Wavelet Packet Bases Yielding the Maximum Coding Gain
Wonha Kim · Journal of the Institute of Electronics Engineers of Korea · 2001
This paper develops the fast dynamic programming technique to construct the subband structure yielding the maximum coding gain for given filter bases and a given limit of implementation complexity. We first derive the unified coding gain which can be applied to non-orthogonal filter basis as well as orthogonal filter basis and to arbitrary subband decompositions. Then, we verify that the unified coding gains in real systems are monotonically increasing function for the implementation complexities which are proportional to the number of subbands. By using this phenomenon, the implementation complexity and the coding gain are treated in the same way as the rate and distortion function. This makes it possible to use the Lagrangian multiplier method for finding the optimal subband decomposition producing the maximum coding gain [or a given limit of implementation complexity.