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, nonperiodic, 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 (≥23 frames per second) performance for a 512×512 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.

Two-dimensional discrete Fourier transform (DFT) is an extensively used and computationally intensive algorithm, with a plethora of applications. 2D images are, in general, nonperiodic 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, specifically for biomedical applications. In this paper we present a novel FPGA-based solution to calculate 2D DFTs with simultaneous edge artifact removal for high-performance applications. Standard approaches for removing these artifacts, using apodization functions or mirroring, either involve removing critical frequencies or necessitate a surge in computation by significantly increasing the image size. We use a periodic plus smooth decomposition-based approach that was optimized to reduce DRAM access and to decrease 1D FFT invocations. 2D FFTs on FPGAs also suffer from the so-called “intermediate storage” or “memory wall” problem, which is due to limited on-chip memory, increasingly large image sizes, and strided column-wise external memory access. We propose a “tile-hopping” memory mapping scheme that significantly improves the bandwidth of the external memory for column-wise reads and can reduce the energy consumption up to 53%. We tested our proposed optimizations on a PXIe-based Xilinx Kintex 7 FPGA system communicating with a host PC, which gives us the advantage of further expanding the design for biomedical applications such as electron microscopy and tomography. We demonstrate that our proposed optimizations can lead to 2.8× reduced FPGA and DRAM energy consumption when calculating high-throughput 4096×4096 2D FFTs with simultaneous edge artifact removal. We also used our high-performance 2D FFT implementation to accelerate filtered back-projection for reconstructing tomographic data.

No abstract