Recursive pruning of the 2D DFT with 3D signal processing applications

A recursively pruned radix-(2×2) two-dimensional (2D) fast Fourier transform (FFT) algorithm is proposed to reduce the number of operations involved in the calculation of the 2D discrete Fourier transform (DFT). It is able to compute input and output data points having multiple and possibly irregularly shaped (nonsquare) regions of support. The computational performance of the recursively pruned radix-(2×2) 2D FFT algorithm is compared with that of pruning algorithms based on the one-dimensional (1D) FFT. The former is shown to yield significant computational savings when employed in the combined 2D DFT/1D linear difference equation filter method to enhance three-dimensional spatially planar image sequences, and when employed in the MixeD moving object detection and trajectory estimation algorithm