  Previous work has shown that high-quality partial volume tissue compartment
maps can be obtained by applying spatially-regularized spectroscopic image
estimation techniques to high-dimensional multicontrast MRI data (e.g.,
diffusion-relaxation data). However, this generally requires substantial
computational complexity. In this work, we propose a more efficient algorithm
to estimate spectroscopic images using spatial regularization. Our algorithm is
based on the linearized alternating directions method of multipliers (LADMM),
and relies on the introduction of novel quadratic penalty terms to
substantially simplify the subproblems that appear within each iteration. We
evaluate this algorithm in a variety of different scenarios
(diffusion-relaxation, relaxation-relaxation, relaxometry, and magnetic
resonance fingerprinting), where we consistently observe substantial
($\sim$3$\times$-50$\times$) speed improvements. We expect that this new
algorithm will reduce barriers to using spatial regularization and
multiparametric contrast-encoded MRI data acquisition methods for partial
volume compartment mapping.
