Cramér–Rao Bound Optimized Subspace Reconstruction in Quantitative MRI

Objective: We extend the traditional framework for estimating subspace bases in quantitative MRI that maximize the preserved signal energy to additionally preserve the Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. Methods: To this end, 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 both the CRB and signal losses during compression. Results: Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with minimal cost to the preserved signal energy, leading to reduced bias and variance of the parameter estimates in simulation. In vivo, improved accuracy and precision are observed in two quantitative neuroimaging applications. Conclusion: The proposed method permits subspace reconstruction with a more compact basis, thereby offering significant computational savings. Significance: Efficient subspace reconstruction facilitates the validation and translation of advanced quantitative MRI techniques, e.g., magnetization transfer and diffusion.