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Nonlinear Tikhonov-regularized Fresnel reconstruction algorithm with (projected) gradient decent

Jens Lucht requested to merge tikhonov-torch into master

Add nonlinear Tikhonov-regularized Fresnel reconstruction algorithm with (projected) gradient decent.

This MR includes 3 major contributions:

  • a projected gradient decent (PGD) algorithm with line search and adaptive stepsizes, i.e. alternating Barlizai-Borwein.
  • differentiable (by PyTorch autograd) functionals for Fresnel regime
  • solver for the nonlinear Tikhonov-regularized Fresnel inverse problem (using the functionals).

This implementation can be used for multi-distance phase retrieval and/or in an astigmatistic setting. Furthermore it supports acceleration by GPU (CUDA) devices, if available.

A user (high-level) interface to this (aligning with CTF API):

from hotopy.phase import Tikhonov

tikhonov = Tikhonov(shape, fresnel_nums)
tikhonov(holograms)

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