Sampling errors in projection reconstruction MRI

Certain kinds of artifacts have been reported when projection reconstruction (PR) techniques are used in magnetic resonance imaging (MRI). These will occur if the spacing between samples in k-space is too large. It has been suggested that PR requires finer k-space sampling than does two-dimensional Fourier reconstruction, and that the usual Nyquist criterion is inadequate. This paper examines this problem, with the conclusion that the Nyquist sampling criterion is adequate to avoid aliasing effects, provided that a band-limited interpolation is used in k-space. This procedure is motivated by analysis of the PR technique as it is commonly implemented in x-ray computed tomography. A related problem is shown to be the construction of a filter function in k-space that gives proper weight to the low spatial frequencies. It is shown that a simple ¿k¿ filter does not satisfy this requirement, and a procedure for deriving a suitable filter is described. The methods are tested in simulated PR profiles of circular disks of two different sizes. It is shown that the combination of the two new methods gives virtually perfect reconstruction for disks up to the size implied by the Nyquist limit.