We investigate the use of direct-Fourier (DF) image reso-called polar expansion algorithm were developed. This article construction in computed tomography and synthetic aperture radar also proposed another reconstruction method based on a direct (SAR). One of our aims is to determine why the convolution-backproapproximation of the Fourier inversion formula, using a 2D trapejection (CBP) method is favored over DF methods in tomography, zoidal rule. In addition, the possibility of reconstruction from a while DF methods are virtually always used in SAR. We show that the concentric-squares raster was discussed. Numerous simple inter-CBP algorithm is equivalent to DF reconstruction using a Jacobianpolators have been tried in DF reconstruction with the results weighted two-dimensional periodic sinc-kernel interpolator. This incompared with CBP [2]. In [3] and [4], the concept of angular terpolation is not optimal in any sense, which suggests that DF algobandlimiting was used to interpolate the polar data onto a rithms using optimal interpolators may surpass CBP in image quality.
Cartesian grid. In [5], a DF reconstruction, using bilinear interpo-We consider use of two types of DF interpolation: a windowed sinc kernel, and the least-squares optimal Yen interpolator. Simulations lation for diffraction tomography, provided image quality that show that reconstructions using the Yen interpolator do not possess was comparable to that produced by the CBP algorithm. Very the expected visual quality, because of regularization needed to pregood reconstruction quality was obtained in [6] and [7] using a serve numerical stability. Next, we show that with a concentricspline interpolator, or a hybrid type of spline interpolator. The squares sampling scheme, DF interpolation can be performed accunotion of ''gridding'' was introduced in [8] as a method of rately and efficiently, producing imagery that is superior to that obtainobtaining optimal inversion of Fourier data. An optimal gridding able by other algorithms. In the case of SAR, we show that the DF function was proposed, and successful results were obtained when method performs very well with interpolators of low complexity. We applied to the tomographic reconstruction problem. In [9], sevalso study DF reconstruction in SAR for trapezoidal grids. We coneral different gridding functions were tried for DF reconstruction, clude that the success of the DF method in SAR imaging is due to and the performances were compared. In [10,11], the linogram the nearly Cartesian shape of the sampling grid.