GSURS: Generalized sparse uniform resampling with application to MRI

We present an algorithm for resampling data from a non-uniform grid onto a uniform grid. Our algorithm termed generalized sparse uniform resampling (GSURS) uses methods from modern sampling theory. Selection of an intermediate subspace generated by integer translations of a compactly supported generating kernel produces a sparse system of equations representing the relation between the nonuniformly spaced samples and a series of generalized samples. This sparse system of equations can be solved efficiently using a sparse equation solver. A correction filter is subsequently applied to the result in order to attain the uniformly spaced samples of the signal. We demonstrate the application of the new method for reconstructing MRI data from nonuniformly spaced k-space samples. In this scenario, the algorithm is first used to calculate uniformly spaced k-space samples, and subsequently an inverse FFT is applied to these samples in order to obtain the reconstructed image. Simulations using a numerical phantom are used to compare the performance of GSURS with other reconstruction methods, in particular convolutional gridding and the nonuniform FFT.