Catalytic multiecho phase unwrapping scheme
A method of nuclear magnetic resonance imaging of an object is disclosed, the method including: receiving MR data including magnitude and phase information generated using an MR scan having a series of different echo times; generating one or more measured MR images based on the MR data; and processing the measured MR images to generate unaliased or substantially unaliased phase information for at least one pixel in the image.
1. A method of nuclear magnetic resonance imaging of an object, the method comprising:
receiving MR data corresponding to n complex MR images generated using an MR scan having a series of n different echo times, where n is an integer equal to two or more, each image corresponding to a respective echo time; and
processing the images to correct phase wrap aliasing, the processing comprising:
i) complex dividing a second image corresponding to a second echo time with a first image corresponding to a first echo time to create a divided complex image;
ii) using a scaling of the phase from the divided complex image to determine a predicted phase at one or more pixels in the second image;
iii) for one or more pixels in the second image, comparing the predicted phase with a measured phase, and
if the difference between the predicted phase and the measured phase lies within a first threshold range, leaving the measured phase in the second image unchanged;
if the difference between the phases lies outside the first threshold range, changing the measured phase value by adding multiples of 2π until the difference falls within the threshold range.
2. The method of claim 1 , the processing further comprising:
iv) using a scaling of the phase from the divided complex image to determine a predicted phase at one or more pixels in a third image by adding the scaling of the phase to the corresponding phase from the second image;
v) for one or more pixels in the third image, comparing the predicted phase with a measured phase, and
if the difference between the predicted phase and the measured phase the predicted phase and the measured phase lies within a first threshold range, leaving the measured phase in the second image unchanged;
if the difference between lies outside the first threshold range, changing the measured phase value by adding multiples of 2π until the difference falls within the threshold range.
3. The method of claim 2 , further comprising, iteratively continuing the processing for images corresponding to the remaining n−3 echo times.
4. The method of claim 3 , wherein, for at least one pixel, a phase difference between the first image and the second image, Δφ(r), computed based on complex division, is added to the phase in the first image to create a predicted phase φ new (r,TE2).
5. The method of claim 4 , comprising, for at least one pixel, comparing the predicted phase φ new (r,TE2) with the measured phase φ(r,TE2) in the second image and:
if φ new (r,TE2)−φ(r,TE2) is less than or equal to a threshold value, leaving (r,TE2) unmodified,
if φ new (r,TE2)−(φ(r,TE2) is greater than a threshold value then adding or subtracting a multiple q of 2π until the absolute value of (φ new (r,TE2)−φ(r,TE2)+/−q2π) is less than a given value ε.
6. The method of claim 5 , wherein ε is about 0.1π or less.
7. The method of claim 5 , wherein, for each pixel, ε is set to απ where α depends on a signal-to-noise ratio (SNR) in a magnitude image corresponding to at least one of the complex images.
8. The method of claim 7 , wherein α is set to a multiple of 1/SNR.
9. The method of claim 8 , wherein α is set to about 3/SNR.
10. The method of claim 1 , wherein a corrected phase from the nth echo is used as input for susceptibility weighted imaging SWI analysis, where n can be any integer between 1 and p where p is the total number of echoes collected in the scan.
11. The method of claim 1 , wherein a corrected phase from the nth echo is used as input for a susceptibility weighted image mapping SWIM analysis, where n can be any integer between 1 and p where p is the total number of echo collected in the scan.
12. The method of claim 1 wherein processing the images to correct phase wrap aliasing comprises:
determining at least one low signal pixel in the MR images having a signal to noise ratio below a threshold level; and
omitting the low signal pixel from the processing.
13. The method of claim 1 , further comprising acquiring the MR data, wherein acquiring the MR data comprises acquiring magnitude data ρ(r) and phase data φ(r) corresponding to each echo time; and further comprising:
Fourier transforming k-space data associated with the MR data to generate MR images.
14. The method of claim 1 , further comprising correcting the first image corresponding to the first echo time to produce an unwrapped phase image.
15. The method of claim 1 , further comprising using MR data corresponding to at least three echo times to correct one or more of the MR images for local field variations.
16. The method of claim 1 , further comprising correcting for eddy current gradient induced phase effects by subtracting a phase value at the center of an image for either or both of even and odd phase images and after creating an anti-aliased image adding an offset back.