Theory for systolizing global computational problems

A theory is presented for rasterizing a class of two-dimensional problems including signal/image processing, computer vision, and linear algebra. The rasterization theory is steered by an isomorphic relationship between the multidimensional shuffle-exchange network (mDSE) and the multidimensional butterfly network (mDBN). Many important multidimensional signal-processing problems can be solved on a mDSE with a solution time approaching known theoretical lower bounds. The isomorphism between mDSE and mDBN is exploited by transforming and mDSE solution into its equivalent mDBN solution. A methodology for rastering the mDBN solution is developed. It turns out that not all mD algorithms can be rasterized. A sufficient condition for algorithm rasterization is given.<>