Compressive sensing (CS) theory has been extensively investigated to reduce MRI scan time and reconstruct high resolution images from down-sampled k-space data by exploiting the sparsity of image in finite difference or transform domain. Recently, many high performance proximal algorithms such as a fast iterative shrinkage-thresholding algorithm (FISTA), alternating direction method of multipliers (ADMM), or a primal-dual algorithm have been considerably studied. However, depending on computing platforms, not only the rate of convergence but also memory usage are very important optimization factors. Hence, the main goal of this study is to perform comparative studies of these algorithms in terms of convergence speed and memory usages in the case of various type penalized 3D CS-MRI experiments including total variation, wavelet transform and patch-based low rank approximation. Our analysis and experimental results showed strength and weakness of each algorithm according to applications.