Philips Res. Lab., Hamburg.
IEEE Trans Med Imaging. 1995;14(3):596-607. doi: 10.1109/42.414625.
The authors explore a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f;. The method involves a window function w; and proceeds in three steps. First, the convolution g;=w;*f; is computed numerically on a Cartesian grid, using the available samples of 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 w;*f; is much less error prone than merely interpolating 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.
作者探索了一种从傅里叶变换的采样版本重建 n 维信号 f 的计算方法 f;。该方法涉及窗口函数 w;，并分三个步骤进行。首先，使用可用的 f; 样本，在笛卡尔网格上数值计算卷积 g;=w;*f;。然后，通过离散傅里叶逆变换计算 wf=g，最后作为 g/w 得到 f。由于卷积的平滑作用，计算 w;*f;比仅仅插值 f;错误要少得多。该方法最初是为射电天文学中的图像重建而设计的，但实际上适用于广泛的重建成像方法，包括磁共振成像和计算机断层扫描。特别是，它为滤波反投影提供了一种快速准确的替代方法。基本方法有几种变体，适用于其他应用，例如对任意采样信号的等距重采样或快速计算 Radon（Hough）变换。
