Generalized approximate message passing algorithms for sparse magnetic resonance imaging reconstruction

A method for reconstructing magnetic resonance imaging data, the method comprising:

• obtaining k-space scan data captured by a MRI system, the k-space scan data being representative of an undersampled region over time;
• and
• reconstructing an image dataset from the k-space scan data by applying generalized approximate message passing (GAMP) to solve an optimization problem which applies a Fourier transform and a wavelet transform to the k-space scan data, wherein GAMP is applied to solve the optimization problem by a process comprising:
• determining a plurality of image distribution values based on the k-space scan data;
• determining a plurality of measurement coefficient values using the plurality of image distribution values and a first belief propagation correction term;
• incorporating a first prior data value into the plurality of measurement coefficient values;
• determining a plurality of sparse coefficient values using the plurality of image distribution values and a second belief propagation correction term;
• incorporating a second prior data value into the plurality of sparse coefficient values;
• and
• updating the plurality of image distribution values based on the plurality of measurement coefficient values and the plurality of sparse coefficient values.

A system for reconstructing magnetic resonance imaging data, the system comprising:

• an imaging device comprising a plurality of coils configured to acquire k-space scan data representative of an undersampled region over time;
• and
• a central control computer unit configured to reconstruct an image dataset from the k-space scan data by applying generalized approximate message passing (GAMP) to solve an optimization problem which applies a Fourier transform and a wavelet transform to the k-space scan data, wherein the central control computer unit applies GAMP is applied using a process comprising:
• determining a plurality of image distribution values based on the k-space scan data,
• determining a plurality of measurement coefficient values using the plurality of image distribution values and a first belief propagation correction term,
• incorporating a first prior data value into the plurality of measurement coefficient values;
• determining a plurality of sparse coefficient values using the plurality of image distribution values and a second belief propagation correction term,
• incorporating a second prior data value into the plurality of sparse coefficient values, and
• updating the plurality of image distribution values based on the plurality of measurement coefficient values and the plurality of sparse coefficient values.