Independent component analysis (ICA) has found great promise in magnetic resonance (MR) image analysis. Unfortunately, two key issues have been overlooked and not investigated. One is the lack of MR images to be used to unmix signal sources of interest. Another is the use of random initial projection vectors by ICA, which causes inconsistent results. In order to address the first issue, this paper introduces a band-expansion process (BEP) to generate an additional new set of images from the original MR images via nonlinear functions. These newly generated images are then combined with the original MR images to provide sufficient MR images for ICA analysis. In order to resolve the second issue, a prioritized ICA (PICA) is designed to rank the ICA-generated independent components (ICs) so that MR brain tissue substances can be unmixed and separated by different ICs in a prioritized order. Finally, BEP and PICA are combined to further develop a new ICA-based approach, referred to as PICA-BEP to perform MR image analysis.