23Na MRI provides important information for many pathologies. However, its low SNR entails low spatial resolutions and long acquisition times. The proposed work reconstructs 3D radially undersampled in vivo 30-channel 23Na head data at B0=7T with a sensitivity encoding using a nonlinear conjugate gradient method (CG-SENSE) including a total variation and a discrete cosine transform. With CG-SENSE using iteratively generated Lagrangian coil sensitivities, image quality and contrast within the object are improved compared to sum of squares (SOS) and adaptive combination (ADC) reconstructions.
CG-SENSE iteratively minimizes the following cost function using a nonlinear conjugate gradient algorithm6:
argmin
where \bf{F} is a non-uniform fast Fourier transform operator (NUFFT)7, \bf{C} are the coil sensitivities, \bf{m} is the reconstructed image, \bf{y} are the k-space data, and \bf{\Psi_i} is one of \bf{N} sparsifying transform operators with \bf{\lambda_i} as its corresponding regularization tuning constant. In this work, three differently generated coil sensitivities \bf{C} are used. The conventional sum of squares (SOS) and birdcage (BC) coil sensitivities are created by dividing each gaussian filtered and phase-corrected individual coil image by the SOS or BC image, respectively. The Lagrangian coil sensitivities \bf{C_{opt}} are generated by minimizing another cost function using an iterative Augmented Lagrangian Method8:
\bf{C_{opt}\stackrel{\wedge}{=} \arg\min_C \frac{1}{2} ||Z-DC||_W^2 + \frac{\lambda}{2}||RC||_2^2 ,}
where \bf{Z} are the single-coil images, \bf{D} is the BC image, \bf{C} are the coil sensitivities, \bf{W} is a weighting matrix, \bf{\lambda} is a regularization tuning constant, and \bf{R} is a finite difference matrix. The weighting matrix acts as a threshold and is subjectively adjusted to the noise level of the BC image. The 23Na data were acquired using a density-adapted 3D radial projection pulse sequence2 on a 7T whole body MR system (MAGNETOM 7T, Siemens Healthcare GmbH, Erlangen, Germany) and a double-resonant 1H/23Na Tx/Rx quadrature volume head coil integrating a 30-channel 23Na Rx phased array (Rapid Biomedical GmbH, Rimpar, Germany). The data were acquired with the following parameters: (Δx)3=(3mm)3, 15000 projections, TE/TR=0.35ms/30ms, α=53°, TA=30min, USF= 1, and Navg=4. The CG-SENSE was regularized with a 3D total variaton3 (TV) and discrete cosine transform (DCT)9. The regularization tuning constants were empirically determined by visual inspection. The reconstruction was initialized with a (72x72x72) matrix of zeros. Convergence was assumed after a maximum of 50 iterations (Figure 1). The performance of CG-SENSE using Lagrangian coil sensitivities is compared to SOS and adaptive combination (ADC) reconstructions. Blurring artifacts in the outer parts of the CG-SENSE images are suppressed by applying a binary mask obtained with the BC data. Furthermore, the influence of the differently generated coil sensitivities on CG-SENSE is analysed.
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9. Myronenko A, NVIDIA, Santa Clara, California, https://sites.google.com/site/myronenko/.