Phase transfer function is numerically small about waveorder

[talonchandler]

My experience with Tikhonov-regularized least squares is that this is expected behavior. Increasing the regularization parameter penalizes large solutions, so it makes sense that your solutions get smaller as you increase the regularization parameter.

@mattersoflight suggests that we rescale $H_{eff}$ to $[0, 1]$, so that $H_{eff} \gg \rho$.

I'm not sure if this will give you the behavior you're looking for. If you 100x H, then your estimate for the phase will need to go down by 100x to match the data, and I expect that your choice of regularization parameter will need to go up by ~100x. (Please prove me wrong!)

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I'm guessing that the desired behavior is regularization-parameter independent reconstructions. If so, we may need to move beyond Tikhonov-regularized least squares with this property specifically in mind.

[ziw-liu]

My experience with Tikhonov-regularized least squares is that this is expected behavior. Increasing the regularization parameter penalizes large solutions, so it makes sense that your solutions get smaller as you increase the regularization parameter.

Now that I think of it in this way, this behavior is indeed expected!

My initial observation with the reconstruction is that with 100x regularization, the image doesn't change significantly other than a 0.01 scaling factor (but all quite usable). So I was suspecting that some numerical issue obscured the smoothing effect.

[ziw-liu]

However I'm still puzzled by how the same observation can be explained by 100x different phase objects (in radians) where the structure remains almost the same.