1. A method of compressed sensing for multi-shell magnetic resonance imaging, the method comprising: providing a magnetic resonance imaging system including a control processor, gradient amplifiers, a radio frequency amplifier, and a pulse generator, wherein the control processor is in communication with the gradient amplifiers, the radio frequency amplifier, and the pulse generator, and wherein the control processor executes computer-readable instructions that cause the control processor to perform the steps of: obtaining magnetic resonance imaging data, the data being sampled along multiple concentric spherical shells, the spherical shells coincident with a plurality of spokes that converge at an origin; constructing a symmetric shell for each respective sampled 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.