__init__(inner_coefficient=1.0, outer_coefficient=1.0, signal_scale=1.0)

A instance-regularization scheme (regularization is described in the Regularization class above).

For the weighted regularization scheme, each pixel is given an ‘effective regularization weight’, which is applied when each set of pixel neighbors are regularized with one another. The motivation of this is that different regions of a pixelization require different levels of regularization (e.g., high smoothing where the no signal is present and less smoothing where it is, see (Nightingale, Dye and Massey 2018)).

Unlike the instance regularization_matrix scheme, neighboring pixels must now be regularized with one another in both directions (e.g. if pixel 0 regularizes pixel 1, pixel 1 must also regularize pixel 0). For example:

B = [-1, 1] [0->1]
[-1, -1] 1 now also regularizes 0

For a instance regularization coefficient this would NOT produce a positive-definite matrix. However, for the weighted scheme, it does!

The regularize weight_list change the B matrix as shown below - we simply multiply each pixel’s effective regularization weight by each row of B it has a -1 in, so:

regularization_weights = [1, 2, 3, 4]

B = [-1, 1, 0 ,0] # [0->1]
[0, -2, 2 ,0] # [1->2] [0, 0, -3 ,3] # [2->3] [4, 0, 0 ,-4] # [3->0]

If our -1’s werent down the diagonal this would look like:

B = [4, 0, 0 ,-4] # [3->0]
[0, -2, 2 ,0] # [1->2] [-1, 1, 0 ,0] # [0->1] [0, 0, -3 ,3] # [2->3] This is valid!
Parameters: coefficients – The regularization coefficients which controls the degree of smoothing of the inversion reconstruction in high and low signal regions of the reconstruction. signal_scale – A factor which controls how rapidly the smoothness of regularization varies from high signal regions to low signal regions.

Methods

 __init__([inner_coefficient, …]) A instance-regularization scheme (regularization is described in the Regularization class above). regularization_matrix_from(mapper) regularization_weights_from(mapper)