Algorithm 3 SPIGH $(\mathbf{Y},\mathbf{C},{\left\{{\mathbf{G}}^{\left(i\right)}\right\}}_{i=1}^3,{\left\{{\mu }_i\right\}}_{i=1}^3,{\left\{s_i\right\}}_{i=1}^3)$a

Initialization: Let Ỹ = C−1/2Y and G̃ ≔ C−1/2G. Set 1 := ｛1, 2, … , p1|S1|｝, where p1 is the number of eigenmodes per patch in 1.

For i = 1, 2, · · · , 3 do:

1: Estimate the cortical activity as ${\widehat{\mathbf{X}}}_i={\widehat{\mathbf{X}}}^{\text{SP–MNE}}(\mathbf{Y},\mathbf{C},{\mathbf{G}}_{{\mathcal{H}}_i}^{(i)},s_i,{\mu }_i)$ with the si-sparse support i ⊂ i.

2: Set i+1 = all the patches in i+1 overlapping i and their nearest neighbors in i+1, and go to step 1.

End

Output: ${\widehat{\mathbf{X}}}^{\text{SPIGH}}≔{\widehat{\mathbf{X}}}^{\text{MNE}}\left(\stackrel{\sim }{\mathbf{Y}},{\stackrel{\sim }{\mathbf{G}}}_{{\mathcal{H}}_4}\right),$i.e., the final estimate is the MNE solution over the central dipoles given by the index set 4.