A method of compressed sensing for multi-shell magnetic resonance imaging includes obtaining magnetic resonance imaging data, the data being sampled along multi-shell spherical coordinates, the spherical coordinates coincident with a plurality of spokes that converge at an origin, constructing a symmetric shell for each respective sampled multi-shell to create a combined set of data, performing a three-dimensional Fourier transform on the combined set of data to reconstruct an image, and de-noising the reconstructed image by iteratively applying a sparsifying transform on non-sampled data points of neighboring shells. The method can also include randomly under-sampling the imaging data to create missing data points. A system configured to implement the method and a non-transitory computer readable medium are also disclosed.