DIRECT-FOURIER RECONSTRUCTION IN TOMOGRAPHY AND SYNTHETIC-APERTURE RADAR

We investigate the use of direct-fourier (DF) image reconstruction in computed tomography and synthetic aperture radar (SAR). One of our aim s is to determine why the convolution-backprojection (CBP) method is f avored over DF methods in tomography, while DF methods are virtually a lways used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobian-weighted two-dimensional periodic sine -kernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms using optimal interpolators may surp ass CBP in image quality. We consider use of two types of DF interpola tion: a windowed sine kernel, and the least-squares optimal Yen interp olator. Simulations show that reconstructions using the Yen interpolat or do not possess the expected visual quality, because of regularizati on needed to preserve numerical stability. Next, we show that with a c oncentric-squares sampling scheme, DF interpolation can be performed a ccurately and efficiently, producing imagery that is superior to that obtainable able by other algorithms. In the case of SAR, we show that the DF method performs very well with interpolators of low complexity. We also study DF reconstruction in SAR for trapezoidal grids. We conc lude that the success of the DF method in SAR imaging is due to the ne arly Cartesian shape of the sampling grid. (C) 1998 John Wiley & Sons, Inc.