Daeun Kim^{1}, Jonathan Polimeni^{2}, Kawin Setsompop^{2}, and Justin Haldar^{1}

^{1}Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, United States, ^{2}Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Harvard Medical School, Massachusetts General Hospital, Charlestown, MA, United States

Noise correlations exist in multi-channel k-space data, and methods to optimally account for this correlation have been used for a long time in image-domain parallel imaging methods like SENSE. However, methods to address noise are not widely-utilized for Fourier-domain parallel imaging methods like GRAPPA, SPIRiT, and AC-LORAKS. In this work, we demonstrate that properly accounting for spatially-varying noise correlation can substantially reduce the noise level of coil-combined images. Further, we demonstrate the existence of previously-unknown correlations between the real and imaginary parts of the noise in reconstructed images. Accounting for this extra correlation can reduce the noise level even further.

This work was supported in part by research grants
NSF CCF-1350563, NIH R01-MH116173, NIH R01-NS074980, and NIH R01-NS089212.

1. Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson Med 1990; 16(2):192-225.

2. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42(5):952-62.

3. Pruessmann KP, Weiger M, Börnert P, Boesiger P. Advances in sensitivity encoding with arbitrary k‐space trajectories. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magn Reson Med 2001;46(4):638-51.

4. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002;47(6):1202-10.

5. McKenzie CA, Ohliger MA, Yeh EN, Price MD, Sodickson DK. Coil‐by‐coil image reconstruction with SMASH. Magn Reson Med 2001;46(3):619-23.

6. Lustig M, Pauly JM. SPIRiT: iterative self‐consistent parallel imaging reconstruction from arbitrary k‐space. Magn Reson Med 2010;64(2):457-71.

7. Zhang J, Liu C, Moseley ME. Parallel reconstruction using null operations. Magn Reson Med 2011;66(5):1241-53.

8. Haldar JP. Autocalibrated LORAKS for fast constrained MRI reconstruction. Proc IEEE ISBI 2015;910-13.

9. Polimeni JR, Setsompop K, Triantafyllou C, Wald LL. Optimal SNR combinations of multi-channel coil data for GRAPPA-reconstructed and time-series EPI data. Proc ISMRM 2013;3355.

10. Robson PM, Grant AK, Madhuranthakam AJ, Lattanzi R, Sodickson DK, McKenzie CA. Comprehensive quantification of signal‐to‐noise ratio and g‐factor for image‐based and k‐space‐based parallel imaging reconstructions. Magn Reson Med 2008;60(4):895-907.

11. Uecker M, Lai P, Murphy MJ, Virtue P, Elad M, Pauly JM, Vasanawala SS, Lustig M. ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA. Magn Reson Med 2014;71(3):990-1001.