Denoising of dynamic magnetic resonance spectroscopic imaging using low rank approximations in the kinetic domain

A magnetic resonance imaging apparatus, comprising:

• a magnet situated to establish an axial magnetic field in a specimen;
• a plurality of coils situated to apply electromagnetic pulse sequences to the specimen;
• a receiver situated to detect electromagnetic signals from the specimen in response to the applied electromagnetic pulse sequences;
• and
• a controller coupled to the plurality of coils so as to selectively apply the electromagnetic pulse sequences and to the receiver to store signal values associated with the detected signals for a plurality of specimen voxels, and process the detected signal by rank reducing a singular value decomposition associated with a matrix representation associated with at least one of the plurality of specimen voxels.

A method, comprising:

• in a magnetic resonance imaging system:
• acquiring a magnetic resonance imaging signal associated with a plurality of chemical shifts for a plurality of voxels at a plurality of times;
• arranging the magnetic resonance imaging signal as a data tensor;
• obtaining a Tucker decomposition of the data tensor;
• and
• spatially or temporally rank reducing the Tucker decomposition to produce spatially or temporally denoised voxel data for each of the plurality of voxels.

A method, comprising:

• in a magnetic resonance imaging system:
• acquiring magnetic resonance imaging signals for a plurality of voxels as a function of at least two parameters;
• arranging the magnetic resonance imaging signals as a data tensor;
• obtaining a Tucker decomposition of the data tensor;
• and
• rank reducing the Tucker decomposition to produce processed voxel data for each of the plurality of voxels based on at least one of the two parameters;
• and