Fast 2D Convolutions and Cross-Correlations Using Scalable Architectures

TL;DR

This paper introduces scalable architectures and algorithms for fast 2D convolutions and cross-correlations by transforming them into 1D operations using DPRT and SVD-LU, optimized for FPGA and Zynq-SOC devices.

Contribution

It presents a novel approach to accelerate 2D convolutions and cross-correlations through transform-based architectures suitable for modern programmable hardware.

Findings

Achieves computation in O(P) to O(P^2) clock cycles depending on resources

Significantly outperforms existing methods on FPGA and Zynq-SOC implementations

Provides scalable architectures adaptable to different resource constraints

Abstract

The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and cross-correlations in the transform domain. This is accomplished through the use of the Discrete Periodic Radon Transform (DPRT) for general kernels and the use of SVD-LU decompositions for low-rank kernels. The approach uses scalable architectures that can be fitted into modern FPGA and Zynq-SOC devices. Based on different types of available resources, for $P\times P$ blocks, 2D convolutions and cross-correlations can be computed in just $O(P)$ clock cycles up to $O(P^2)$ clock cycles. Thus, there is a trade-off between performance and required numbers and types of resources. We provide implementations of the proposed architectures using modern programmable devices (Virtex-7 and Zynq-SOC). Based on the amounts and types of required resources, we show that the proposed approaches significantly outperform current methods.