Optimal sampling in array-based image formation

Abstract

In some types of imaging, the signal is strictly limited in one domain while sampling takes places in another. If sampling is done in a rectangular array pattern at sub-Nyquist density, the array must be dithered to sample the image at the Nyquist density in each dimension. However, the Nyquist density oversamples the image due to the nonrectangular support in the transform domain. We present an efficient algorithm for optimizing the dithering pattern so that the image can be reconstructed as reliably as possible from a periodic nonuniform set of samples, which can be obtained from a dithered rectangular-grid array. Taking into account the transform support of the image, we sequentially eliminate the least informative array recursively until the minimal number of arrays remain.