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It has been previously shown that high-quality partial volume tissuecompartment maps can be obtained by combining multiparametric contrast-encodedMRI data acquisition methods with spatially-regularized spectroscopic imageestimation techniques. However, the advantages of this combined approachgenerally come at the expense of substantial computational complexity. In thiswork, we propose a new algorithm to solve this kind of estimation problem moreefficiently. Our algorithm is based on the linearized alternating directionsmethod of multipliers (LADMM), and relies on the introduction of novelquadratic penalty terms to substantially simplify the subproblems that must besolved at each iteration. We evaluate this algorithm on a variety of differentestimation problems (diffusion-relaxation, relaxation-relaxation, relaxometry,and magnetic resonance fingerprinting), where we consistently observesubstantial (roughly 5$\times$-80$\times$) speed improvements. We expect thatthis new faster algorithm will lower practical barriers to using spatialregularization and multiparametric contrast-encoded MRI data acquisitionmethods for partial volume compartment mapping.

An Efficient Algorithm for Spatial-Spectral Partial Volume Compartment Mapping with Applications to Multicomponent Diffusion and Relaxation MRI