As a fundamental application of compressive sensing, magnetic resonance imaging (MRI) can be efficiently achievable by exploiting fewer $k$-space measurements. Firstly, we consider solving the TV2L1 based magnetic resonance imaging (MRI) signal reconstruction problem by an efficient alternating direction method of multipliers. By sufficiently utilizing the problem's special structure, we manage to make all subproblems either possess closed-form solutions or can be solved via Fast Fourier Transforms (FFTs), which makes the cost per iteration is very low; Secondly, we consider a constrained total generalized variation and shearlet transform based model for MRI reconstruction, which is usually more undemanding and practical to identify appropriate tradeoffs than its unconstrained counterpart. The second model can be facilely and efficiently solved by the strictly contractive Peaceman-Rachford splitting method, which generally outperforms some state-of-the-art algorithms when solving separable convex programming. Numerical simulations demonstrate that the sharp edges and grainy details in magnetic resonance images can be well reconstructed from the under-sampling data.