Module src.heuristics

Functions associated with the computation of the heuristic regularization parameters to be used in SARA, HyperSARA or Faceted HyperSARA.

src.heuristics.compute_noise_level(Ny, Nx, n_channels, std_noise, algo_version, Qx, Qy, overlap_size, squared_operator_norm)

Compute heuristic order of magnitude for the regularization parameters involved in SARA [Abdulaziz2019] or Faceted HyperSARA [Thouvenin2021].

Parameters

  • Ny (int) – Spatial image size along axis y.

  • Nx (int) – Spatial image size along axis y.

  • n_channels (int) – Number of frequency channels.

  • std_noise (double) – Estimate of the standard deviation of the white Gaussian noise affecting the data.

  • algo_version (string) – Imaging problem considered (HyperSARA, 'hs' or Faceted HyperSARA 'fhs'),

  • Qx (int) – Number of spatial facets along spatial axis x.

  • Qy (int) – Number of spatial facets along spatial axis y.

  • overlap_size (int[2]) – Overlap size between consecutive facets along each axis (y and x).

  • squared_operator_norm (double) – Square of the measurement operator norm, \(\|\Phi\|_2^2\).

Returns

  • sig (double) – Heuristic value sparsity regularization parameter.

  • sig_bar (double) – Heursitic value low-rankness regularization parameter.

  • mu_chi (double) – Heuristic estimate of the mean of the noise using a \(\chi_2\) approximation. (?)

  • sig_chi (double) – Heuristic estimate of the standard deviation of the noise using a \(\chi_2\) approximation. (?)

  • sig_sara (double) – Heuristic estimate of the noise level (standard deviation) when transferred to the SARA dictionary domain. (?)

src.heuristics.compute_noise_level_sara(std_noise, squared_operator_norm)

Estimate noise level in the SARA domain.

Return an estimate of the noise standard deviation transferred successively from the data to the image domain, then to the SARA domain.

Parameters

  • std_noise (double) – Noise standard deviation in the data domain.

  • squared_operator_norm (double) – Squared norm of the measurement operator.

Returns

sig – Estimate of the noise level.

Return type

double