Cram\'er-Rao Bound Optimized Temporal Subspace Reconstruction in Quantitative MRI

Purpose: To extend the traditional framework for estimating temporal bases that maximize preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve image quality in the quantitative maps. Theory and Methods: We introduce an approximate compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of the CRB in addition to the signal loss typically minimized by SVD-derived bases. Comparisons to the traditional SVD basis are analyzed in two quantitative neuroimaging applications in vivo. Results: The proposed approach improves the preservation of the CRB across all biophysical parameters with negligible cost to the preserved signal energy in simulation. Improved accuracy and SNR at smaller subspace sizes are observed in vivo compared to the traditional SVD basis. Conclusion: Minimizing CRB loss in addition to preserving signal fidelity permits the use of smaller basis sizes in subspace reconstruction, offering significant computational savings.