A medical image consists of tissue contrast and boundary information. Due to frequency differences, they can be separated by gradient encoding in MRI data acquisition. Typically the contrast information is concentrated within the center k-space while the outer k-space data provide most of the boundary information. In the presented work, we develop an approach to accelerating MRI by taking advantage of this non-uniform k-space distribution of tissue contrast and boundary information. A high-speed imaging framework developed in our previous works^1,2, "correlation imaging", is used to reconstruct images from undersampled data. By converting image reconstruction into the estimate of correlation functions between parallel data acquisition channels, correlation imaging can benefit from both coil sensitivity encoding and tissue boundary sparsity. Our experiments demonstrate that this approach can provide an imaging speed gain over parallel imaging by utilizing more information in image reconstruction.

A correlation function between two channels i and j is defined as:

c_^ij(k) = sum{ [d_i(k'+k)] conjugate[d_j(k')] }_{over k'} (1),

where {d_i(k), i=1,2,…,N} represents N-channel fully sampled k-space data. In correlation imaging^1,2, if these correlation functions were estimated, they can be used to form a set of linear equations for resolving a set of k-space filters. Image reconstruction is given by the linear convolution of the resolved filters and the collected data. It should be noted that Equation 1 quantifies the correlation of k-space data samples in a distance of k. Typically, the correlation functions from a set of more correlated k-space data are more dominated by a spread-out pattern around the k-space center (i.e., higher correlation values between samples in a larger distance). It is thus possible to predict the performance of correlation imaging based on the k-space pattern of correlation functions.

In a medical image, tissue boundary is sparser than tissue contrast. As a result, image content sparsity increases with tissue boundary information from center to outer k-space. Since image sparsity may enhance data correlation, a more dominant spread-out pattern can be seen in the correlation functions calculated from an outer k-space region than those from a center k-space region (Figure 1). This indicates that outer k-space data are more correlated and correlation imaging performs better in outer k-space than in center k-space. For this reason, we can undersample outer k-space more than center k-space for improved imaging acceleration. As illustrated by Figure 2(a), the presented work divides the whole k-space into multiple local regions. Each region is undersampled uniformly and the undersampling factors increase from the center to the outer k-space regions. Image reconstruction is performed iteratively in a region-by-region fashion and every region is reconstructed using a different set of correlation functions (Figure 2b).

To validate the approach, a set of 3D brain imaging data was collected using a T1-weighted ultrafast gradient echo sequence (FOV 240x240x240 mm, matrix 240x240x154, TR/TE 9.3/4.6 ms, flip angle 8°, data acquisition time ~6 minutes) on a 3T clinical MRI scanner. The coil array for data collection had 8 elements uniformly positioned around the anatomy. The fully-sampled data were manually undersampled to simulate imaging acceleration. SENSE, GRAPPA, and SPIRiT were used as reference approaches.

Figure 2 shows the reconstruction results for a center sagittal slice with a net imaging acceleration factor of 10 (corresponding to a data acquisition time of ~30 seconds). Compared with SENSE, GRAPPA, and SPIRiT, correlation imaging with non-uniform undersampling gives better image quality and smaller errors. This improvement is found in all the images generated from the collected 3D data.Parallel imaging acceleration is dependent on coil sensitivity encoding and limited by the channel number. Using an 8-channel coil with an acceleration factor of 10, our experiments were run beyond the parallel imaging limit. For this reason, parallel imaging performs poorly. In contrast, the presented approach performs well. This gain should be attributed to the following two factors. First, region-by-region reconstruction can utilize both coil sensitivity encoding and the priori information about medical images, i.e., the k-space variation of data correlation associated with tissue boundary sparsity. Second, as shown in Figure 2(right), the reconstructed data are iteratively used as a constraint on the estimation of correlation functions for the reconstruction of each k-space region in correlation imaging. This additional constraint can translate more information about data correlation into image reconstruction for improved correlation imaging.We have developed a new correlation imaging approach to utilizing tissue boundary sparsity to accelerate MRI. It is demonstrated that this approach can provide a gain in imaging acceleration over parallel imaging.