Sparse sampling methods have emerged as effective tools to accelerate cardiac magnetic resonance imaging (MRI).Low-rank model-based cardiac imaging uses a predetermined temporal subspace for image reconstruction from highly undersampled (k, t)-space data and has been demonstrated effective for high-speed cardiac MRI. The accuracy of the temporal subspace isa key factor in these methods, yet little work has been published on data acquisition strategies to improve subspace estimation. This paper investigates the use of non-Cartesian k-space trajectories to replace the Cartesian trajectories that are omnipresent but are highly sensitive to readout direction. We also propose "self-navigated" pulse sequences that collect both navigator data (for determining the temporal subspace) and imaging data after every RF pulse, allowing for even greater acceleration. We investigate subspace estimation strategies through analysis of phantom images and demonstrate in vivo cardiac imaging in rats and mice without the use of ECG or respiratory gating. The proposed methods achieved 3-D imaging of wall motion, first-pass myocardial perfusion, and late gadolinium enhancement in rats at 74 frames/s,as well as 2-D imaging of wall motion in mice at 97 frames/s.