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.

翻译：卷积是信号处理中最重要的运算之一，通常涉及大规模数组且计算耗时显著。此外，实际应用中，待卷积处理的信号数据可能受到噪声污染。本文提出一种新方法，采用量化张量列（QTT）格式计算卷积，并利用QTT分解去除数据中的噪声。我们通过合成孔径雷达（SAR）处理中常见的含sinc核的数学模型验证了方法性能，完整展示了原始数据数组分解、卷积计算以及将数据重新格式化为完整数组的全部计算成本。