SNR-optimality of sum-of-squares reconstruction for phased-array magnetic resonance imaging. Larsson, E. G., Erdogmus, D., Yan, R., Principe, J. C., & Fitzsimmons, J. R. Journal of Magnetic Resonance, 163(1):121–123, July, 2003.
SNR-optimality of sum-of-squares reconstruction for phased-array magnetic resonance imaging [link]Paper  doi  abstract   bibtex   
We consider the commonly used ‘‘Sum-of-Squares’’ (SoS) reconstruction method for phased-array magnetic resonance imaging with unknown coil sensitivities. We show that the signal-to-noise ratio (SNR) in the image produced by SoS is asymptotically (as the input SNR ! 1) equal to that of maximum-ratio combining, which is the best unbiased reconstruction method when the coil sensitivities are known. Finally, we discuss the implications of this result.
@article{larsson_snr-optimality_2003,
	title = {{SNR}-optimality of sum-of-squares reconstruction for phased-array magnetic resonance imaging},
	volume = {163},
	issn = {10907807},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S1090780703001320},
	doi = {10.1016/S1090-7807(03)00132-0},
	abstract = {We consider the commonly used ‘‘Sum-of-Squares’’ (SoS) reconstruction method for phased-array magnetic resonance imaging with unknown coil sensitivities. We show that the signal-to-noise ratio (SNR) in the image produced by SoS is asymptotically (as the input SNR ! 1) equal to that of maximum-ratio combining, which is the best unbiased reconstruction method when the coil sensitivities are known. Finally, we discuss the implications of this result.},
	language = {en},
	number = {1},
	urldate = {2022-03-31},
	journal = {Journal of Magnetic Resonance},
	author = {Larsson, Erik G. and Erdogmus, Deniz and Yan, Rui and Principe, Jose C. and Fitzsimmons, Jeffrey R.},
	month = jul,
	year = {2003},
	pages = {121--123},
}

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