Algorithms for Efficient Computation of Convolution

Abstract

Convolution is an important mathematical tool in both fields of signal and image processing. It is em-ployed in filtering, denoising, edge detection, correlation, compression, deconvolution, simulation, and in many other applications. Although the concept of convolution is not new, the efficient computation of convolution is still an open topic. As the amount of processed data is constantly increasing, there is considerable request for fast manipulation with huge data. Moreover, there is demand for fast algorithms which can exploit computational power of modern parallel architectures. The aim of this chapter is to review the algorithms and approaches for computation of convolution with regards to various properties such as signal and kernel size or kernel separability (when pro-cessing n-dimensional signals). Target architectures include superscalar and parallel processing units (namely CPU, DSP, and GPU), programmable architectures (e.g. FPGA), and distributed systems (such as grids). The structure of the chapter is designed to cover various applications with respect to the signal size, from small to large scales.