Quantitative MRI (qMRI) provides biomarkers of microstructural properties of brain tissue and enables in-vivo monitoring of microscopic brain changes due to disease in patient populations. The widely used Multi Parameter Mapping qMRI protocol allows the computation of MTSat, PD, R1, and R2* maps. While it allows the assessment of multiple brain tissue properties, its acquisition time is excessive for clinical applications. Here, we propose a compressed sensing scheme based on a Cartesian spiral-phyllotaxis readout to reduce the total acquisition time of 1mm isotropic whole brain maps. A preliminary qualitative and quantitative validation is performed on healthy subjects.