The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition

Perfect reconstruction quadrature mirror filters (PR QMF’s) have been proposed as structures suitable for hierarchical subband coding [ ll-[4], and also for multiresolution signal decomposition as might be used in image pyramid coding [5]. More recently, multiresolution signal decomposition methods are being examined from the standpoint of the discrete wavelet transform for continuous-time signals [6]-[8]. In this paper, we describe a class of orthogonal binomial filters that provide basis functions for a perfect reconstruction bank of finite impulse response QMF’s. The orthonormal wavelet filters derived by Daubechies 171 from a discrete wavelet transform approach are shown to be the same as the solutions inherent in the binomial-based filters. The energy compaction performance of the binomial QMF decomposition is computed and shown to be better than the DCT for the Markov source models, as well as real-world images considered. The proposed binomial structure is efficient, simple to implement on VLSI, and suitable for multiresolution signal decomposition and coding applications.