A Framework for SPICE MRSI Reconstruction Posterior Uncertainty Quantification

Purpose: Low-rank reconstruction methods such as SPICE substantially improve Magnetic Resonance Spectroscopic Imaging (MRSI) reconstruction quality. However, SPICE does not provide an estimate of reconstruction uncertainty. A framework for posterior uncertainty estimation in SPICE reconstruction is proposed, hereafter referred to as the framework. Theory and Methods: A Laplace approximation is used to estimate the covariance of the reconstructed spatial coefficients. This covariance is propagated through the spectral basis and spectral fitting to obtain metabolite concentration uncertainty. Matrix-free Hessian--vector products and voxel-wise conjugate-gradient estimation are used to avoid explicit construction or inversion of the full Hessian, making the method tractable. Results: Validation using repeated in vivo 7 T MRSI acquisitions showed that the estimated posterior uncertainty exhibited spatial and spectral patterns similar to those of empirical repeated-scan uncertainty. Experiments further demonstrated how spatial regularization and k-space undersampling affect the estimated uncertainty. Conclusion: The framework provides a practical framework for uncertainty quantification when using SPICE reconstruction of MRSI. It could be adapted to other regularised low-rank reconstruction methods.