2D Discrete Fourier Transform with Simultaneous Edge Artifact Removal for Real-Time Applications

Two-Dimensional (2D) Discrete Fourier Transform (DFT) is a basic and computationally intensive algorithm, with a vast variety of applications. 2D images are, in general, non-periodic, but are assumed to be periodic while calculating their DFTs. This leads to cross-shaped artifacts in the frequency domain due to spectral leakage. These artifacts can have critical consequences if the DFTs are being used for further processing. In this paper we present a novel FPGA-based design to calculate high-throughput 2D DFTs with simultaneous edge artifact removal. Standard approaches for removing these artifacts using apodization functions or mirroring, either involve removing critical frequencies or a surge in computation by increasing image size. We use a periodic-plus-smooth decomposition based artifact removal algorithm optimized for FPGA implementation, while still achieving real-time ($\ge$23 frames per second) performance for a 512$\times$512 size image stream. Our optimization approach leads to a significant decrease in external memory utilization thereby avoiding memory conflicts and simplifies the design. We have tested our design on a PXIe based Xilinx Kintex 7 FPGA system communicating with a host PC which gives us the advantage to further expand the design for industrial applications.