In this paper we propose a new methodology - nonlinear I/O index space transformations based on I/O index space data dependence analysis, and apply it to the design of the efficient and real-time structures for the 2-D Discrete Multi-wavelet Transform (MWT). Multi-wavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multi-wavelets offer the advantages of combining symmetry, orthogonality, and short support, properties not mutually achievable with scalar wavelet systems. As a new pomising technique, 2-D MWT has lately been applied to image processing applications with a superior performance that surpasses the performance of well-known scalar wavelet transforms using pyramid algorithms, implemented by tree-structured filter banks. The difference is that multi-wavelets have several scaling functions and the filter banks in MWT are composed of matrix-valued filters with vector sequences as their inputs and outputs. Corresponding to each multi-wavelet system is a matrix-valued multirate filterbank, or multifilter, which has "taps" that are rxr matrices. The non-memory-based, hardware-efficient, and real-time implementations of 2-D transforms are much desirable in the application specific systems for image/video processing systems. However, there are not yet such designs reported for the implementation of 2-D multiwavelet transform, one of the reasons for which is the complicated computation structure of the algorithm. This paper shows how to take advantage of I/O index space based data dependence analysis in designing an efficient and real-time system with minimum storage and 100% hardware utilization for a class of 2-D multi-wavelet transform.
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