Partially parallel imaging (PPI) is an emerging technology in compressive magnetic resonance imaging (MRI). By partial data acquisition PPI reduces scan time significantly, but this reduction leads to serious aliasing artifacts in images. To improve the clinic applicability of this techniques we developed several efficient algorithms for total variation-based image reconstruction. In this talk I will introduce Bregman operator splitting (BOS) with Barzilai-Borwein (BB) stepsize, and BOS with variable step size from a line search strategy to improve the performance of BOS. The comparison of those methods will also be presented.