dMRI-Lab 1.0
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Functions | |
function | micro2shsqrtodf (in dwifile, in gifile, in bifile, in lambdaparfile, in lambdaperpfile, in ffile, in shfile, in nitfile, in mufile, in varargin) |
The SH coefficients of the ODF and the SH coefficients of its squared root are analytically related via Wigner's symbols, and the latter are estimated by solving a bi-quadratic problem with a unique quadratic restriction (if the ODF has unit mass, the coefficients vector of its squared root has norm 1). | |
function micro2shsqrtodf | ( | in | dwifile, |
in | gifile, | ||
in | bifile, | ||
in | lambdaparfile, | ||
in | lambdaperpfile, | ||
in | ffile, | ||
in | shfile, | ||
in | nitfile, | ||
in | mufile, | ||
in | varargin ) |
The SH coefficients of the ODF and the SH coefficients of its squared root are analytically related via Wigner's symbols, and the latter are estimated by solving a bi-quadratic problem with a unique quadratic restriction (if the ODF has unit mass, the coefficients vector of its squared root has norm 1).
Computes the SH coefficients of the squared root of a unit mass, strictly non-negative ODF that best fits the multi-shell attenuation signal atti (with gradients table gi and b-values bi) according to the convolutional model:
atti(u,b) = (1-f)*exp(-b*Diso) + f*Integral_{S}Phi(v)exp(-b*((lpar-lperp)(u*v)^2+lperp))dv,
where lpar and lperp parameterize the impulse response as an elemental rank-2 tensor, f stands for the partial volume fraction of water confined in the neural axons, and Diso is the free-water (extra-cellular) diffusivity. Phi(v) is the ODF whose squared root we aim at estimating, so that Phi(v) will be non-negative at any possible point of its continuous domain. The coefficients of the ODF itself can be retrieved from the coefficients of its squared root (i.e. the output of this function) with a call to sh2squaredsh. NOTE: if the squared root of the ODF spands up to an even order L, then the ODF spans up to an order 2L.
dwifile | A string specifying the file containing the diffusion-weighted images. |
gifile | A string specifying the file containing the gradient directions. |
bifile | A string specifying the file containing the b-values. |
lambdaparfile | A string specifying the file containing the elemental diffusivity along the parallel direction. |
lambdaperpfile | A string specifying the file contanining the elemental diffusivity along the perpendicular direction. |
ffile | A string specifying the file containing the partial volume fraction. |
shfile | A string specifying the file to save the SH coefficients of the squared root of the ODF at each imaged voxel. |
nitfile | A string specifying the file to save the number of iterations it took to converge or -1 if convergence failed. |
mufile | A string specifying the file to save the value of the Lagrange multiplier if Newton-Raphson's method is used. |
varargin | Optional arguments passed as -name value pairs. |
Mandatory Inputs:
Optional Arguments:
Sanity Checks On The Micro-Structure Model:
Advanced parameters:
Examples: