Abstract
Convolutions are one of the most important operations in signal processing. They often involve large arrays and require significant computing time. Moreover, in practice, the signal data to be processed by convolution may be corrupted by noise. In this paper, we introduce a new method for computing the convolutions in the quantized tensor train (QTT) format and removing noise from data using the QTT decomposition. We demonstrate the performance of our method using a common mathematical model for synthetic aperture radar (SAR) processing that involves a sinc kernel and present the entire cost of decomposing the original data array, computing the convolutions, and then reformatting the data back into full arrays.
Original language | English |
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Pages (from-to) | 1 |
Number of pages | 22 |
Journal | Communications in Analysis and Computation |
Early online date | 11 Mar 2023 |
DOIs | |
Publication status | E-pub ahead of print - 11 Mar 2023 |