  We extend the traditional framework for estimating subspace bases that
maximize the preserved signal energy to additionally preserve the Cram\'er-Rao
bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and
precision in the quantitative maps. To this end, we introduce an
\textit{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. Compared to the traditional SVD approach,
the proposed method better preserves the CRB across all biophysical parameters
with negligible 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, permitting the use of smaller basis sizes in subspace
reconstruction and offering significant computational savings.
