Phase retrieval example

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No files, tests, or entry points are named in the issue. Start by reviewing the existing Pylops examples and solver documentation to identify how they handle complex-valued data and regularization. Done means a minimal example script demonstrates the stated phase-retrieval objective with a sparsity prior and a Split-Bregman or ISTA solver.

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描述

Hi,
I would like to leverage Pylops for the domain of 'phase retrieval', but I don't know how to start on this. A typical phase retrieval problem has the following form:

|| y - | F^-1{ K * F{x}} | ||^2 + lam || |x| ||^1

y is a measured real-valued 2D image
x is an unknown complex-valued 2D image
F and F^-1 are the forward and backward 2D Fourier transforms
K is a complex-valued 2D kernel (predefined dense matrix), defined in Fourier domain

So, intuitively, complex-valued 2D image x is 2D convoluted (by multiplication in Fourier domain) and only the magnitude is fitted to the known real-valued 2D image y. This problem is ill-posed, and needs regularization. I would e.g. like to add a sparsity prior on the magnitude of x and solve this using a Split-bregman solver or ISTA solver.

Would it be possible for you to provide a minimal example script that does just that, to point me in the right direction?

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