A method for reconstructing an image of a subject from multi-coil data acquired with an array of radio frequency (“RF”) receiver coils that form a part of a magnetic resonance imaging (“MRI”) system without the need for coil sensitivity calibration is provided. A coil data set is acquired for each of the RF receiver coils, for example, by undersampling k-space. A set of image blocks that defines the location and size of each of a plurality of image blocks in the image domain is then selected. The acquired coil data sets and selected image block set are then used to jointly estimate a coil image for each of the plurality of RF receiver coils while promoting locally-low rank structure in the coil images. These coil images are then combined to produce the target image of the subject.