Image Reconstruction Using Novel Two-Dimensional Fourier Transform

Abstract

Reconstruction of a signal from its subset is used in various contexts in the field of signal processing. Image reconstruction is one such example which finds widespread application in face recognition, medical imaging, computer vision etc. Image reconstruction is computationally complex, and efficient implementations need to exploit the parallelism inherent in this operation. Discrete Fourier Transform (DFT) is a widely used technique for image reconstruction. Fast Fourier Transform (FFT) algorithms are used to compute DFTs efficiently. In this paper we propose a novel two dimensional (2D) Fast Fourier Transform technique for efficient reconstruction of a 2D image. The algorithm first applies 1D FFT based on radix-\(4^n\) along the rows of the image followed by same FFT operation along columns, to obtain a 2D FFT. Radix-\(4^n\) technique used here provides significant savings in memory required in the intermediate stages and considerable improvement in latency. The proposed FFT algorithm can be easily extended to three dimensional and higher dimensional FFTs. Simulated results for image reconstruction based on this technique are presented in the paper. 64 point FFT based on radix-\(4^3\) has been implemented using 130nm CMOS technology and operates at a maximum clock frequency of 350 MHz.