Logo of halHAL - Archives Ouvertes - Home page.

TABLE II.

Notations for variables and parameters used in the model for a given parcel inline-graphic halms753873ig3 with Jγ voxels.

Notation Definition Dimension
Variables y j ∈ ℝ N Observed BOLD signal at voxel j N
b j ∈ ℝ N Acquisition noise vector at voxel j N
h γ = {hd Δ t , d = 0 … D} ∈ ℝ D +1 HRF sampled at Δ t D + 1
a j m NRL at voxel j for condition m 1
a m = { a j m , j P γ } J γ n NRLs for condition m Jγ
q j m { 0 , 1 } Activation class for voxel j and condition m 1
q m = { q j m , j P γ } { 0 , 1 } J γ Activation classes for condition m Jγ

Unknown Parameters j ∈ ℝ O Low frequency drifts for voxel j O
Γ j ∈ ℝ N × N Noise precision matrix for voxel j N × N
μ m = {μ 0 m , μ 1 m } ∈ ℝ2 Mixture model means for NRLs in condition m 2
v m = { v 0 m , v 1 m } + 2 Mixture model variances for NRLs in condition m 2
βm ∈ ℝ+ Potts regularization parameter for condition m 1
v h ∈ ℝ+ HRF prior parameter 1

Fixed X m ∈ {0, 1} N × D +1 Binary stimulus occurrence matrix for condition m N × (D + 1)
P ∈ ℝ N × O Low frequency orthonormal function basis N × O
IEEE Trans Med Imaging. 2013 May; 32(5): 821–37.
Published online 2012 October 19. doi: 10.1109/TMI.2012.2225636.