Myelin water fractions (MWF) can provide biomarkers for many brain disorders. Multiple-spin-echo (MSE) is considered as gold standard for obtaining MWF. However, its clinical application is limited by its long acquisition time. Efficient undersampling and exploiting the redundancy in the contrast images of MSE can decrease the acquisition time. We propose a subspace based image reconstruction technique designed for reconstructing contrast images from highly undersampled MSE acquisition, so that it can be used for MWF mapping. We evaluate it for different signal-to-noise ratios for up to acceleration factor of 16 and show its feasibility for accelerating acquisition beyond parallel imaging.