Systems and methods for compressed sensing for multi-shell magnetic resonance imaging

A non-transitory computer readable medium having stored thereon instructions which when executed by a processor cause the processor to perform a method of multi-shell magnetic resonance imaging, the method comprising:

• 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.

A system for compressed sensing for multi-shell magnetic resonance imaging, the system comprising:

• 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;
• the control processor configured to execute computer-readable instructions that cause the control processor to perform a method including:
• obtain 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;
• construct a symmetric shell for each respective sampled shell to create a combined set of data;
• perform a three-dimensional Fourier transform on the combined set of data to reconstruct an image;
• and
• de-noise the reconstructed image by iteratively applying a sparsifying transform on non-sampled data points of neighboring shells.