Extension of finite-support extrapolation using the generalized series model for MR spectroscopic imaging

In magnetic resonance (MR) imaging, limited data sampling in κ-space leads to the well-known Fourier truncation artifact, which includes ringing and blurring. This problem is particularly severe for MR spectroscopic imaging, where only 16-24 points are typically acquired along each spatial dimension. Several methods have been proposed to overcome this problem by incorporating prior information in the image reconstruction. These include the generalized series (GS) model and the finite-support extrapolation method. This paper shows the connection between finite-support extrapolation and the GS model. In particular, finite-support extrapolation is a limiting case of the GS model, when the only available prior information is the support region. The support region refers to those image portions with nonzero intensities, and it can be estimated in practice as the nonbackground region of an image. By itself, the support region constitutes a rather weak constraint that may not lead to considerable resolution gain. This situation can be improved by using additional prior information, which can be incorporated systematically with the GS model. Examples of such additional prior information include intensity estimates of anatomical structures inside the support region.