On Compression Techniques for Computing Convolutions

Eduardo Sany Laber, Pedro Moura, Lucas Pavanelli

Abstract: The computation of convolutions is a fundamental problem that arises in applications from different fields as digital signal processing, image processing and string processing, among others. Here, we provide an in-depth investigation of the potential of Run Length Encoding and Lempel-Ziv based methods for efficiently computing convolutions between a sequence of patterns of a fixed shape/size and a given image. Our contribution consists in developing new methods and variants of existing ones and providing (extensive) empirical evaluations of them. Our fastest method outperforms a highly optimized implementation based on Fast Fourier Transform for small patterns.