Denoising Convolution Algorithms and Applications to SAR Signal Processing

TL;DR

This paper introduces a novel method for efficient convolution computation and noise removal in SAR signal processing using quantized tensor train (QTT) format, significantly reducing computational costs.

Contribution

It presents a new QTT-based approach for convolution and denoising in SAR data, enhancing efficiency and accuracy over traditional methods.

Findings

Effective noise removal in SAR signals

Reduced computational complexity for convolutions

Successful application to synthetic aperture radar models

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.