A pixel is an artifact: On the necessity of zero‐filling in fourier imaging1. (19th March 2013) - Zhu, Xiaolu; Tomanek, Boguslaw; Sharp, Jonathan
Abstract: MR imaging data is sometimes presented in a "patchwork quilt" format with individual pixels visible as squares of uniform intensity. This phenomenon often arises by default from an image space convolution (performed implicitly by the graphics system) used to convert the sparse point sampling of the spatial domain offered by the discrete Fourier transform (DFT) into a sufficiently dense sampling to allow assignment of an intensity value to each addressable point on the display device. Typical examples are fMRI maps, spectroscopic images and zoomed‐in views. These square patches are image structure not present in the object, i.e., artifacts. This form of image display is studied by both an image analysis method and by Fourier analysis. Image formation by display of the 2D DFT of an acquired k‐space matrix as a 2D pixel array is a poor reconstruction because it does not ensure a faithful representation of the spatial frequency content actually present in the data. By analysis of the visual appearance of 2D pixel arrays we show that there are two principal effects: (a) attenuation of higher spatial frequencies (i.e., low‐pass filtering); (b) introduction of artifactual high frequency image structure. These effects can lead to very poor performance with an artifact/signal ratio of over 200% in the corners of 2D k‐space. Generated k‐space maps demonstrate that both detrimental effects increase radially in k‐space. The simple remedy is to zero‐fill (resulting in image interpolation) until individual pixels become invisible in the displayed image. Alternatively, data modeling may be used. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part 42A: 32–44, 2013.