In array imaging (1, 2), partial phase encoding steps can be replaced by the spatially localized sensitivity encoding of each component coil in the phased array (3). Various reconstruction algorithms, like SENSE (sensitivity encoding) (4) or GRAPPA (generalized autocalibrating partially parallel acquisitions) (5), can be then used to recover the missing data in this partially parallel imaging (PPI) technology. With a phased array consisting of four or eight surface receive coils, two- to four- or even higher fold acceleration has previously been obtained in 2D imaging using parallel imaging alone without perceptible aliasing artifacts and significant signal-to-noise-ratio (SNR) penalty(6). Limited to the phase encoding (PE) direction, the maximal achievable acceleration factor (AF) is generally limited by the ill-posed inverse problem involved in the data reconstruction(4), originating from the geometric properties of the coil setup; the number of component coils in the array also sets a theoretical AF upper bound to 1D PPI.

Several benefits can be achieved by combining PPI with 3D Fourier MRI. First, applying PPI along the two PE directions separately, a net acceleration can be obtained as the product of the two independent AFs along the two PE directions(7). In the case of high AF PPI, the inverse problem conditioning of PPI reconstruction can be improved by splitting the high net AF into two smaller AFs in each PE(7). The SNR degradation can then be improved, compared to using the same net AF along one PE in 1D PPI. Second, the SNR loss issue of PPI in 3D MRI may be less important due to the intrinsic high SNR of 3D MRI. Third, PPI can directly relieve the prominent long scan time issue of 3D MRI, compared to the corresponding 2D version.

2D PPI for 3D MRI was first reported in (7). Called 2D SENSE therein, this 2D PPI works in the image domain using the SENSE (4) unfolding method for each slice along each acceleration direction separately. An improvement was subsequently presented by Breuer *et al*. using an optimal sampling strategy, CAIPIRINHA (controlled aliasing in parallel imaging results in higher acceleration) (8–10), to control the aliasing along the PPI direction, which does not have enough sensitivity variation for an effective PPI reconstruction. Inherited from SENSE, the 2D SENSE reconstruction quality depends on the explicitly estimated sensitivity map, which may be hard to obtain in some regions with very low SNR in whole brain imaging, and its estimation error will be inevitably transmitted into the final reconstruction. Without explicit sensitivity estimation, Blaimer *et al*. (11) gave a *k*-space-based 2D PPI using the GRAPPA operator (12). In this approach, the missing *k*-space data were recovered by applying GRAPPA reconstruction along the two PE directions sequentially, and part of the precedently recovered data were used in the second PPI reconstruction step, which may cause extra noise due to error propagation from the imperfect reconstruction in the first PPI reconstruction step. Moreover, using the original GRAPPA reconstruction approach, it only considered the correlation information carried by the neighbors from one *k*-space dimension, while ignoring the abundant information from other surrounding neighbors in the 3D *k*-space (13, 14).

In this paper, a previously proposed improved GRAPPA data reconstruction method, multicolumn multiline interpolation (MCMLI) (13, 14) was generalized to the surrounding neighbors-based autocalibrating partially parallel imaging (SNAPPI) and used in 2D PPI reconstruction for 3D MRI. Several 2D PPI reconstruction strategies were presented, using separable 2D PPI reconstruction through SNAPPI reconstruction along each PE direction independently as in (11) and nonseparable 2D PPI reconstruction also through SNAPPI, in the 3D *k*-space or the hybrid *k* and image space (hybrid space). In the case where one PE direction does not have enough sensitivity variation for regular PPI, CAIPIRINHA type sampling strategy (8–10) was also used to control the aliasing along that direction. Both simulations and in vivo experiments were conducted to evaluate the presented 2D PPI approaches.