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dwi2SH | |
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convert base diffusion-weighted images to their spherical harmonic representation.
This program outputs the spherical harmonic decomposition for the set measured signal attenuations. The signal attenuations are calculated by identifying the b-zero images from the diffusion encoding supplied (i.e. those with zero as the b-value), and dividing the remaining signals by the mean b-zero signal intensity. The spherical harmonic decomposition is then calculated by least-squares linear fitting.
Note that this program makes use of implied symmetries in the diffusion profile. First, the fact the signal attenuation profile is real implies that it has conjugate symmetry, i.e. Y(l,-m) = Y(l,m)* (where * denotes the complex conjugate). Second, the diffusion profile should be antipodally symmetric (i.e. S(x) = S(-x)), implying that all odd l components should be zero. Therefore, this program only computes the even elements.
Note that the spherical harmonics equations used here differ slightly from those conventionally used, in that the (-1)^m factor has been omitted. This should be taken into account in all subsequent calculations.
Each volume in the output image corresponds to a different spherical harmonic component, according to the following convention:
[0] Y(0,0)
[1] Im {Y(2,2)}
[2] Im {Y(2,1)}
[3] Y(2,0)
[4] Re {Y(2,1)}
[5] Re {Y(2,2)}
[6] Im {Y(4,4)}
[7] Im {Y(4,3)}
etc...
syntax: dwi2SH [ options ] dwi SH
| dwi | the input diffusion-weighted image. |
| SH | the output spherical harmonics coefficients image. |
| -grad encoding | specify the diffusion-weighted gradient scheme used in the acquisition. The program will normally attempt to use the encoding stored in image header.
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| -lmax order | set the maximum harmonic order for the output series. By default, the program will use the highest possible lmax given the number of diffusion-weighted images.
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| -normalise | normalise the DW signal to the b=0 image | ||
| -info | display information messages. | ||
| -quiet | do not display information messages or progress status. | ||
| -debug | display debugging messages. | ||
| -help | display this information page and exit. | ||
| -version | display version information and exit. |