Compressed sensing and the use of phased array coils in ²³Na MRI: a comparison of a SENSE-based and an individually combined multi-channel reconstruction

Purpose: To implement and to evaluate a compressed sensing (CS) reconstruction algorithm based on the sensitivity encoding (SENSE) combination scheme (CS-SENSE), used to reconstruct sodium magnetic resonance imaging (²³Na MRI) multi-channel breast data sets. Methods: In a simulation study, the CS-SENSE algorithm was tested and optimized by evaluating the structural similarity (SSIM) and the normalized root-mean-square error (NRMSE) for different regularizations and different undersampling factors (USF = 1.8/3.6/7.2/14.4). Subsequently, the algorithm was applied to data from in vivo measurements of the healthy female breast (n = 3) acquired at 7 T. Moreover, the proposed CS-SENSE algorithm was compared to a previously published CS algorithm (CS-IND). Results: The CS-SENSE reconstruction leads to an increased image quality for all undersampling factors and employed regularizations. Especially if a simple 2^nd order total variation is chosen as sparsity transformation, the CS-SENSE reconstruction increases the image quality of highly undersampled data sets (CS-SENSE: SSIM_USF=7.2 = 0.234, NRMSE_USF=7.2 = 0.491 vs. CS-IND: SSIM_USF=7.2 = 0.201, NRMSE_USF=7.2 = 0.506). Conclusion: The CS-SENSE reconstruction supersedes the need of CS weighting factors for each channel as well as a method to combine single channel data. The CS-SENSE algorithm can be used to reconstruct undersampled data sets with increased image quality. This can be exploited to reduce total acquisition times in ²³Na MRI.