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International Journal of Reconfigurable Computing
Volume 2018, Article ID 1403181, 17 pages
Research Article

Algorithm and Architecture Optimization for 2D Discrete Fourier Transforms with Simultaneous Edge Artifact Removal

1Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
2Structural Cellular Biology Unit, Okinawa Institute of Science and Technology (OIST), Okinawa, Japan

Correspondence should be addressed to Faisal Mahmood; ude.uhj@mlasiaf

Received 18 December 2017; Revised 11 May 2018; Accepted 10 June 2018; Published 6 August 2018

Academic Editor: João Cardoso

Copyright © 2018 Faisal Mahmood et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 . 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 reduced FPGA and DRAM energy consumption when calculating high-throughput 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.