In preclinical research, micro-CT is commonly used to provide anatomical information; however, there is significant interest in using this technology to obtain functional information in cardiac studies. The fastest acquisition in 4D cardiac micro-CT imaging is achieved via retrospective gating, resulting in irregular angular projections after binning the projections into phases of the cardiac cycle. Under these conditions, analytical reconstruction algorithms, such as filtered back projection, suffer from streaking artifacts. Here, we propose a novel, multi-resolution, iterative reconstruction algorithm inspired by robust principal component analysis which prevents the introduction of streaking artifacts, while attempting to recover the highest temporal resolution supported by the projection data. The algorithm achieves these results through a unique combination of the split Bregman method and joint bilateral filtration. We illustrate the algorithm’s performance using a contrast-enhanced, 2D slice through the MOBY mouse phantom and realistic projection acquisition and reconstruction parameters. Our results indicate that the algorithm is robust to under sampling levels of only 34 projections per cardiac phase and, therefore, has high potential in reducing both acquisition times and radiation dose. Another potential advantage of the multi-resolution scheme is the natural division of the reconstruction problem into a large number of independent sub-problems which can be solved in parallel. In future work, we will investigate the performance of this algorithm with retrospectively-gated, cardiac micro-CT data.