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Add wavefield preconditioner #584
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You need to take the square root of the sum, not the sum of the square roots. |
How stupid of me, thank you! This now works as expected :) |
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The secret sauce of the LSQ-ML algorithm seems to be what they call average update directions:
In reality this is just scaling the ML update directions by 1 / Lipschitz constant for the exit wave error as shown by Andy Maiden et al in "Further improvements to the ptychographical iterative engine". Note that 1/L is known to be the optimal step size for gradient descent on convex functions in the math optimization literature:
https://math.stackexchange.com/questions/3587312/the-biggest-step-size-with-guaranteed-convergence-for-constant-step-size-gradien
This PR adds an option to ML called "wavefield_precond" that enables this "average update preconditioner". The following results on Moonflower suggests that this is highly effective at accelerating ML as shown in the images below.
Vanilla ML (all parameters default, 200 iterations):
ML with wavefield_precond=True (all other parameters default, 200 iterations):