Imaging sampling below the Nyquist density without aliasing

For multidimensional band-limited functions, the Nyquist density is defined as that density corresponding to maximally packed spectral replications. Because of the shape of the support of the spectrum, however, sampling multidimensional functions at Nyquist densities can leave gaps among these replications. In this paper we show that, when such gaps exist, the image samples can periodically be deleted or decimated without information loss. The result is an overall lower sampling density. Recovery of the decimated samples by the remaining samples is a linear interpolation process. The interpolation kernels can generally be obtained in closed form. The interpolation noise level resulting from noisy data is related to the decimation geometry. The greater the clustering of the decimated samples, the higher the interpolation noise level is.