Direct-Fourier reconstruction in tomography and synthetic aperture radar

We investigate the use of direct-Fourier (DF) image reconstruction in computerized tomog-raphy and synthetic aperture radar (SAR). One of our aims is to determine why the convolution-backprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobian-weighted 2-D periodic sinc-kernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the least-squares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentric-squares sampling scheme, DF interpolation can be performed accurately and eeciently, producing imagery that is superior to that obtainable 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 conclude that the success of the DF method in SAR imaging is due to the nearly-Cartesian shape of the sampling grid.