Notations for variables and parameters used in the model for a given parcel with Jγ voxels.
Notations for variables and parameters used in the model for a given parcel with Jγ voxels.
Notation | Definition | Dimension | |
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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 | |
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NRL at voxel j for condition m | 1 | |
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NRLs for condition m | Jγ | |
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Activation class for voxel j and condition m | 1 | |
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Activation classes for condition m | Jγ | |
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Unknown Parameters | ℓ 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 | |
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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 | |
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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 |