Fast computation of convolution operations via low-rank approximation |
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| Affiliation: | 1. Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China;2. Key Laboratory of Marginal Sea Geology, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, China;1. Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea;2. Department of Mathematics, Sookmyung Women’s University, Seoul 04310, Republic of Korea |
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| Abstract: | Methods for the approximation of 2D discrete convolution operations are derived for the case when a low-rank approximation of one of the input matrices is available. Algorithms based on explicit computation of discrete convolution and on the Fast Fourier Transform are both described. Applications of the described methods to the computation of cross-correlation and autocorrelation are discussed and illustrated by examples. Both theory and numerical experiments show that the use of low-rank approximations makes it possible to determine accurate approximations of convolution, cross-correlation, and autocorrelation operations at competitive speeds. |
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