THE GRIDDING METHOD FOR IMAGE-RECONSTRUCTION BY FOURIER TRANSFORMATION

This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform ($) over cap f. The method involves a window function ($) over cap w and proceeds in three steps. First, the convolution ($) over cap g = ($) over cap w * ($) over cap f is computed numerically on a Cartesian grid, using the available samples of ($) over cap f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating ($) over cap w * ($) over cap f is much less error prone than merely interpolating ($) over cap f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography, In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform.