A method for improving image quality of image data includes analyzing, for each of a plurality of voxels of image data, a set of entries of a dictionary, wherein an entry represents a mapping between a lower resolution patch of voxels and a corresponding higher resolution patch of voxel or a local neighborhood around a voxel, deriving, for each of the plurality of voxels, a subspace based on the analysis, wherein the subspace is for one of the mapping or the local neighborhood, and restoring target image data based on the subspaces, wherein the target image data is image data with higher image resolution or reduced image noise.