Efficient image reconstruction using partial 2D Fourier transform

In this paper we present an efficient way of doing image reconstruction using the 2D discrete Fourier transform (DFT). We exploit the fact that in the frequency domain, information is concentrated in certain regions. Consequently, it is sufficient to compute partial 2D Fourier transform where only m times m elements of an N times N image are nonzero. Compared with the traditional row-column (RC) decomposition algorithm, the proposed algorithm enables us to reconstruct images with significantly smaller computation complexity at the expense of mild degradation in quality. We also describe the implementation of the new reconstruction algorithm on a Xilinx Virtex-II Pro-100 FPGA. For 512 times 512 natural and aerial images, this implementation results in 68% reduction in the number of memory accesses and 76% reduction in the total computation time compared to the RC method.