Magnetic resonance image reconstruction using analytic image representation

Partial k-space acquisition is a subject of great interest in magnetic resonance imaging (MRI). This type of acquisition usually consists of, in addition to the positive half of k-space, acquiring a number of negative frequencies beyond the k-space center, thus requiring an increase of acquisition time. Furthermore, the quality of the reconstructed image depends on the number of negative frequencies acquired. To date it has not been demonstrated that the non-acquisition of negative frequencies of k-space can produce useful reconstructed images. We propose a novel approach for reconstructing MR images from partial k-space. It is based on the notion of analytic image and presents the particularity of using only exactly half of k-space without involving any negative frequencies or phase estimation. Furthermore, it can be implemented at no cost. The benefits are illustrated by experiments on both simulated and real human brain image.