Methods for fat quantification with correction for noise bias
Methods are disclosed for calculating a fat fraction corrected for noise bias of one or more voxels of interest using a magnetic resonance imaging (MRI) system. A plurality of image data sets are obtained each corresponding to NMR k-space data acquired using a pulse sequence with an individual associated echo time t n . A system of linear equations is formed relating image signal values to a desired decomposed calculated data vector having a component such as a water and fat combination having zero mean noise, or having a real fat component and a real water component. A fat fraction is calculated from at least one component of the decomposed calculated data vector. In another embodiment, the system of linear equations is normalized and can directly estimate a fat fraction or a water fraction having reduced noise bias.
1. A method for calculating a fat fraction for one or more voxels of interest using a magnetic resonance imaging (MRI) system, the steps of the method comprising:
a) obtaining a plurality of image data sets with the MRI system, each of the plurality of image data sets corresponding to k-space data acquired using a pulse sequence with an individual associated echo time, wherein each image data set includes a corresponding image signal value at each of a plurality of voxels;
b) forming an image signal vector for each voxel of interest, the image signal vector including a corresponding image signal value from each of the plurality of image data sets,
c) calculating, for each voxel of interest, at least one of a real-valued water signal component, a real-valued fat signal component, and a real-valued combined water and fat signal component by solving a system of linear equations in which a phase of water and a phase of fat are set equal to each other and that relates the image signal vector and respective echo times to at least two of a real-valued water signal component, a real-valued fat signal component, and a real-valued combined water and fat signal component; and
d) calculating, for each voxel of interest, a fat fraction that is corrected for noise bias using the at least one of a real-valued water signal component, a real-valued fat signal component, and a real-valued combined water and fat signal component calculated in step c).
2. The method of claim 1 , wherein the at least one of a real-valued water signal component and a real-valued fat signal component calculated in step c) has noise with a substantially zero mean.
3. The method of claim 1 , wherein solving the system of linear equations includes performing a least squares estimation.
4. The method of claim 3 , wherein performing the least squares estimation includes the calculation of a pseudo-inverse of a matrix.
5. The method of claim 2 , wherein the at least one of a real-valued water signal component and a real-valued fat signal component calculated in step c) that has noise with a substantially zero mean is a real-valued fat component, and step d) includes calculating the fat fraction by dividing the real-valued fat signal component by the real-valued combined water and fat signal component.
6. The method of claim 2 , wherein the at least one of a real-valued water signal component and a real-valued fat signal component calculated in step c) that has noise with a substantially zero mean is a real-valued water component, and step d) includes calculating the fat fraction by calculating a water fraction and subtracting the water fraction from one.
7. The method of claim 6 , wherein the water fraction is calculated by dividing the real-valued water signal by the real-valued combined water and fat signal.
8. The method of claim 1 , wherein step c) includes calculating a real-valued combined water and fat signal component, and the system of linear equations relates the image signal vector and respective echo times to a real-valued water signal component and the real-valued combined water and fat signal.
9. The method of claim 8 , wherein step c) further includes calculating the real-valued water signal component by solving the system of linear equations.
10. The method of claim 1 , wherein step c) includes calculating a real-valued combined water and fat signal, and the system of linear equations relates the image signal vector and respective echo times to a real-valued fat signal component and the real-valued combined water and fat signal.
11. The method of claim 10 , wherein step c) further includes calculating the real-valued fat signal component by solving the system of linear equations.