Synopsis

Compressed Sensing has allowed a significant reduction of acquisition times in MRI. However, to maintain high signal-to-noise ratio during acquisition, CS is usually combined with parallel imaging (PI). Here, we propose a new self-calibrating MRI reconstruction framework that handles non-Cartesian CS and PI. Sensitivity maps are estimated from the data in the center of k-space while MR images are iteratively reconstructed by minimizing a nonsmooth criterion using the proximal optimized gradient method, which converges faster than FISTA. Comparison with L1-ESPIRiT suggests that our approach performs better both visually and numerically on 8-fold accelerated Human brain data collected at 7 Tesla.

Introduction

Materials and Methods

Setup. Four healthy volunteers were scanned with a 7T system (Siemens Healthineers, Erlangen, Germany) and a 1Tx/32Rx head coil (Nova Medical, Wilmington, USA). All subjects signed a written informed consent form and were enrolled in the study under the approval of our institutional review board.

Sequence and k-space trajectories. A modified 2D T2*-weighted interleaved GRE sequence was acquired for an in-plane resolution of 390 ㎛ with the following parameters: TR=550ms, TE=30ms and FA=25° for one axial slice of 3 mm-thickness, matrix size N=512x512. The Sparkling trajectory (Fig. 1) was composed of 64 shots, each comprising 512 samples during a readout of 30.72 ms. Although Sparkling was implemented prospectively, here we used this sampling scheme retrospectively from fully sampled Cartesian data. Hence, the number of measurements was M=32,768 and the subsampling factor R=N/M=8.

Sensitivity maps extraction. Sensitivity maps information lies in the low-frequency domain, hence variable-density trajectories like radial or sparkling intrinsically handle this information and allow self-calibration without fully sampling the k-space center. Our sensitivity map estimation method thus extracts the 10% central surface of the measured k-space. Then, low frequency NxN coil images were reconstructed applying the NFFT operator to the data completed by zero-filling. Third, the square root of the Sum of Squares (SSOS) was computed. Fourth, the sensitivity maps were estimated by the pixelwise ratio between image coils and the SSOS.

Reconstruction. The CS-PI reconstruction problem consists of minimizing a penalized least square criterion involving the data collected over the 32 channels and a L1-norm penalty term promoting sparsity in the wavelet domain. The balance between the two is controlled by paramter λ>0 whose optimal setting was performed using a grid search procedure over [10^-7, 10^-4]. Forward-Backward, FISTA and POGM optimization algorithms are summarized in Fig. 2.

Results

Sensitivity maps. Fig. 3 illustrates three sensitivity maps extracted using either our method or L1-ESPIRIT. Because of the SVD decomposition involved in L1-ESPIRIT, the sensitivity profiles are smoother as compared to ours, which clearly delineate the FOV part illuminated by each receiver coil. Moreover, our approach is faster since it costs 1min as compared to 10min for L1-ESPIRIT on the same architecture and Matlab-R2017 software.

MR image reconstruction. MR images were reconstructed from Sparkling data either using our approach or L1-ESPIRiT. Although full FOV images look very similar (Fig. 4(a)-(c)), the respective zooms (Fig. 4(d)-(f)) show that the dark stripes in the white matter are lost in the L1-ESPIRiT image whereas they are well preserved using our self-calibrating solution. In addition, our POGM algorithm converged in 2.5 min whereas L1-ESPIRiT took about 5 min.

Convergence speed. The same experimental setup was used to compare the three algorithms. As reported in Fig. 5, FISTA and POGM decrease faster than FB even though they show some “Nesterov ripples”. Interestingly, POGM decreases a little bit faster than FISTA during the first tens of iterations.

Discussion and Conclusion

Acknowledgements

References