Recursive Merge-Filter Algorithm for Computing the Discrete Wavelet Transform

We present a new wavelet transform algorithm with a data flow that can fully exploit the locality property of wavelets. This leads to highly optimized fine grained wavelet coding algorithms, in terms of pipelining performance, flexible data granularity and reliability of transmission. It can be used by all wavelet coding methods, and has been demonstrated to improve the performance of the most successful ones. We propose a new bottom-up Embedded Zerotree Wavelet (EZW) image coding algorithm, and demonstrate a 5-10% speedup over EZW, by means of close coupling between the new wavelet transform algorithm and the EZW encoding. The Recursive Merge Filter (RMF) operator introduced in this paper reduces the complexity of creating larger DWTs of size 2N, from smaller ones of size N, by O(logN). Because this is a frequent operation in the training process of the wavelet based hierarchical vector quantization (W-HVQ) method, the result is a significant speedup overall. The RMF algorithm facilitates new fine grained wavelet codecs, based on EZW encoding of sub-images using our new bottom-up algorithm this can give rise to future standards along the lines of “wavelet JPEG” and “wavelet MPEG”.