Table 1.

Symbols used in FORNI

Symbol	Definition
vi	Basis direction
i, q	Index for basis directions
N	Number of basis directions
G	Dictionary matrix containing attenuation terms
m, n, m0, m1	Index for voxels
M	Number of voxels
wm,n	Voxel similarity between m and n
𝒩m	Neighborhood of m
Dm	Diffusion tensor at m
ym	Diffusion signal at m
fm	Mixture fraction at m
f̂m	Estimated mixture fraction at m
f̃m	Normalized mixture fraction estimate at m
fm,i	Entry of fm
fth	Mixture fraction threshold
wm,j	FO at m
j	Index for FOs
𝒲m	The set of all FOs at m
um,p	Likely FO at m
p	Index for likely FOs
𝒰m	The set of all likely FOs at m
Cm	Weighting matrix at m
Cm,i	Diagonal entry of Cm
α, β, μ	Parameters in FORNI
rm,n(i)	Basis-neighbor similarity
Rm(i)	Aggregate basis-neighbor similarity
θR	An angle threshold
t	Index for iterations
Np	Number of voxels processed in parallel