Deconvolution‐interpolation gridding (DING): Accurate reconstruction for arbitrary k‐space trajectories

A simple iterative algorithm, termed deconvolution-interpolation gridding (DING), is presented to address the problem of reconstructing images from arbitrarily-sampled k-space. The new algorithm solves a sparse system of linear equations that is equivalent to a deconvolution of the k-space with a small window. The deconvolution operation results in increased reconstruction accuracy without grid subsampling, at some cost to computational load. By avoiding grid oversampling, the new solution saves memory, which is critical for 3D trajectories. The DING algorithm does not require the calculation of a sampling density compensation function, which is often problematic. DING's sparse linear system is inverted efficiently using the conjugate gradient (CG) method. The reconstruction of the gridding system matrix is simple and fast, and no regularization is needed. This feature renders DING suitable for situations where the k-space trajectory is changed often or is not known a priori, such as when patient motion occurs during the scan. DING was compared with conventional gridding and an iterative reconstruction method in computer simulations and in vivo spiral MRI experiments. The results demonstrate a stable performance and reduced root mean square (RMS) error for DING in different k-space trajectories.