pySPFM._solvers.spatial_regularization.spatial_tikhonov

pySPFM._solvers.spatial_regularization.spatial_tikhonov#

spatial_tikhonov(estimates, data, masker, niter, dim, lambda_, mu)[source]#

Spatial regularization technique with Tikhonov regularization as in Total Activation.

This function computes the tikhonov regularization

\(\\mathbf{F(x)} = \\min \\| \\mathbf{y} - \\mathbf{x} \\|^2 + \\lambda \\cdot \\| \\Delta \\mathbf{x}\\|^2\).

Delta is the laplacian operator delta[n] = [1 -2 1]; so symmetric, in matrix form \(\\Delta^T = \\Delta\).

Parameters:
  • estimates (ndarray) – Estimates (output of temporal regularization).

  • data (ndarray) – Observations.

  • masker (nilearn.maskers.NiftiMasker) – Masker image to unmask and mask estimates (2D to 4D and back).

  • niter (int) – Number of iterations to perform spatial regularization.

  • dim (int) – Slice-wise regularization with dim = 2; whole-volume regularization with dim=3. Default = 3.

  • lambda_ (float) – Spatial regularization parameter. Default = 1.

  • mu (float) – Step size (small, ~0.01)

Returns:

final_estimates (ndarray) – Estimates of activity-inducing or innovation signal after spatial regularization.