Systolic arrays for the Haar transform

Abstract

A reformulation of the Haar transform algorithm is used to design systolic arrays for data compression. First a triangular array is developed for the normalised 1-D transform and it is then extended to produce an inverse transformation. Area-efficient and unrolled array designs employing the 1-D arrays are used to develop high-throughput, area-efficient arrays with 100%, efficiency which produce one transformed data item per clock cycle. The 1-D designs are then incorporated into a 2-D design for image compression using row and column operations. Finally the arrays are augmented with a simple thresholding design which produces a compressed lossy output. High throughput can be achieved. A complete compression/decompression of the data can be performed using the arrays in conjunction with a thresholding array which adds O(m2) cells and an additional latency of 2m steps. The design is scalable in that m can be chosen to suit manufacturing capabilities.