Discrepancy-based adaptive regularization for GRAPPA reconstruction

Purpose: To develop a novel regularization method for GRAPPA by which the regularization parameters can be optimally and adaptively chosen.

Materials and methods: In the fit procedures in GRAPPA, the discrepancy principle, which chooses the regularization parameter based on a priori information about the noise level in the autocalibrating signals (ACS), is used with the truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization, and its performance is compared with the singular value (SV) threshold method and the L-curve method, respectively by axial and sagittal head imaging experiments.

Results: In both axial and sagittal reconstructions, normal GRAPPA reconstruction results exhibit a relatively high level of noise. With discrepancy-based choices of parameters, regularization can improve the signal-to-noise ratio (SNR) with only a very modest increase in aliasing artifacts. The L-curve method in all of the reconstructions leads to overregularization, which causes severe residual aliasing artifacts. The 10% SV threshold method yields good overall image quality in the axial case, but in the sagittal case it also leads to an obvious increase in aliasing artifacts.

Conclusion: Neither a fixed SV threshold nor the L-curve are robust means of choosing the appropriate parameters in GRAPPA reconstruction. However, with the discrepancy-based parameter-choice strategy, adaptively regularized GRAPPA can be used to automatically choose nearly optimal parameters for reconstruction and achieve an excellent compromise between SNR and artifacts.