On the Feasibility of Fast Fourier Transform Separability Property for Distributed Image Processing

Given the high algorithmic complexity of applied-to-images Fast Fourier Transforms (FFT), computational-resource-usage efficiency has been a challenge in several engineering fields. Accelerator devices such as Graphics Processing Units are very attractive solutions that greatly improve processing times. However, when the number of images to be processed is large, having a limited amount of memory is a serious problem. This can be faced by using more accelerators or using higher-capability accelerators, which implies higher costs. The separability property is a resource in hardware approaches that is frequently used to divide the two-dimensional FFT work into several one-dimensional FFTs, which can be simultaneously processed by several computing units. Then, a feasible alternative to address this problem is distributed computing through an Apache Spark cluster. However, determining the separability-property feasibility in distributed systems, when migrating from hardware implementations, is not evident. For this reason, in this paper a comparative study is presented between distributed versions of two-dimensional FFTs using the separability property to determine the suitable way to process large image sets using both Spark RRDs and DataFrame APIs.