Improved Compressed Sensing Reconstruction for Equidistant K-Space by Sampling Decomposition and Its Application in Parallel MR Imaging

INTRODUCTION Compressed Sensing (CS) is of significant interest for fast MR imaging because it can be used with k-space sub-sampling and parallel imaging [1,2]. Although implementations were made to combine CS with parallel imaging, the incoherent sampling requirement is a bottleneck for implementation because most k-space sampling in parallel imaging is coherent. Thus, a direct plug-in of CS to parallel imaging, especially in the case of equidistant k-space sampling, is not feasible. We propose a simple method to eliminate this problem and illustrate the idea using GRAPPA reconstruction [3]. A perceptual difference model (Case-PDM) was used to quantitatively evaluate image quality [4] in experiments. METHODS Given a coherent parallel imaging k-space data, we break the coherence through applying random masks to decompose the data along phase encoding (PE) into multiple incoherent subsets. Sampling within each subset is randomized. All k-space sampled data were utilized. CS reconstruction [5] was applied on each subset to recover a full k-space data. Finally, all CS reconstructed full k-space datasets were aggregated to produce the final, aliasing reduced, k-space data. To combine with GRAPPA, we use the full k-space reconstruction from the previous step to calibrate the GRAPPA complex weights. (We call this method “CS+GRAPPA” hereafter). Both phantom and in vivo parallel MR cardiac data were used. RESULTS Coherent aliasing artifact due to equidistant under-sampling cannot be reduced by CS without decomposition, but can be significantly reduced by CS with just 2 decompositions (Fig. 1c). More decompositions further reduce aliasing artifacts (Fig. 1d) at the expense of computation time. CS+GRAPPA significantly improved image quality as compared to the standard method for the same high-speed (reduction factor = 8) imaging condition by both visual inspection and PDM score (Fig. 2). CS+GRAPPA can work with much higher reduction factors and fewer ACS lines that are not feasible for the standard method (Fig. 2). Alternatively, comparable image quality can be achieved with many fewer data samples. DISCUSSION We conclude that CS can be applied to equidistant k-space sampling by the proposed method and that the sampling scheme can be applied to CS in parallel MR imaging. The proposed method significantly reduced coherent aliasing artifact using just 2 decompositions. By sequentially combining with our method, GRAPPA imaging can be significantly improved in image quality and sped up with fewer k-space samples, and potentially even no ACS lines. A great application opportunity is in dynamic MR imaging, particularly, cardiac imaging, where reduction factors could be very high. The computational cost of our method should not be a limitation for its application due to development of fast CS algorithms, parallelization of the CS processes, and GPU acceleration. The results could be further improved through using edge detection guided reconstruction [6]. ACKNOWLEDGEMENTS This work was supported under NIH grant R01-EB004070, the Research Facilities Improvement Program Grant NIH C06RR12463-01, and an Ohio Biomedical Research and Technology Transfer award, “The Biomedical Structure, Functional and Molecular Imaging Enterprise.” REFERENCES [1] Candes et al., IEEE Trans. Inf. Theory, 2002 [2] Donoho et al., IEEE Trans. Inf. Theory, 2006 [3] Griswold et al., MRM 2002 [4] Miao et al., Medical Physics, 2008 [5] Yang et al., Technical Report, TR08-27, CAAM, Rice University. [6] Guo et al., MICCAI, 2008.