We previously presented a framework to reconstruct 3D non-rigid motion-fields from highly undersampled k-space data by exploiting the lower-dimensional nature of motion-fields. Here, a quantitative comparison with a well-established image-based motion estimation is performed on 3D abdomen images. To also exploit temporal compressibility the framework is extended to reconstructions of spatio-temporal non-rigid motion-fields at high frame-rate, and validation is performed on 2D+t abdomen cine-acquisitions. Additionally, a dedicated non-Cartesian 3D trajectory was employed to prospectively acquire highly undersampled k-space data, and reconstruct 3D+t head motion at 16Hz. High quality respiratory/head motion-fields are obtained and the framework outperforms the fully-sampled image-based motion estimation even for undersampling up to 8x.