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Marchenko-Pastur Virtual Coil Compression (MP-VCC)
Gregory Lemberskiy1, Jelle Veraart1, Benjamin Ades-aron1, Els Fieremans1, and Dmitry S Novikov1
1Radiology, NYU School of Medicine, New York, NY, United States
We propose a method of virtual coil compression using random matrix theory, MP-VCC, in which the Marchenko-Pastur distribution defines how many virtual coils may be discarded without loss beyond the PCA precision. MP-VCC is evaluated for PF, regular undersampling, and MB acceleration. 
Marchenko-Pastur Virtual Coil Compression (MP-VCC) For the aliased region of MB=2 experiment, we display a (A) local spatial patch, $$$X_C$$$, (B) its VC basis $$$X_{VC}$$$, and (C) its eigenvalue spectrum with the MP distribution in black. (D) Spatially varying virtual coil maps, $$$P_C$$$, are shown for every experiment.
Statistics of Discarded VCs. Properties of the normalized residuals $$$r=(\text{noisy}-\text{denoised})/\sigma$$$, characterizing the discarded VCs, are evaluated via (A,B) histograms showing Gaussian distribution of $$$r$$$; and (C,D) power spectrum analysis, showing no memory along the measurement dimension (temporal power-spectrum $$$\Gamma(\omega)$$$ of residuals is flat) and marginal low-frequency bias along the spatial dimension (spatial power-spectrum $$$\Gamma(k)$$$ of residuals flat for almost all $k$)