Abstract
The phase retrieval problem, where one aims to recover a complexvalued image from farfield intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closedform gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for datarich imaging modalities. We use a reversemode automatic differentiation (AD) framework to implement an efficient matrixfree version of the LevenbergMarquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear leastsquare minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the leastsquare applications. Since we use AD, we only need to specify the physicsbased forward model for a specific imaging application; the first and secondorder derivative terms are calculated automatically through matrixvector products, without explicitly forming the large Jacobian or GaussNewton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained "blind"ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to stateoftheart first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms bestinclass firstorder methods: It provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested firstorder algorithms.
Original language  English (US) 

Pages (fromto)  2301923055 
Number of pages  37 
Journal  Optics Express 
Volume  29 
Issue number  15 
DOIs  
State  Published  Jul 19 2021 
ASJC Scopus subject areas
 Atomic and Molecular Physics, and Optics
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A matrixfree LevenbergMarquardt algorithm forefficient ptychographic phase retrieval
KANDEL, S. (Contributor), MADDALI, S. (Contributor), NASHED, Y. S. G. (Contributor), HRUSZKEWYCZ, S. O. (Contributor), Jacobsen, C. (Contributor) & ALLAIN, M. (Contributor), The Optical Society, 2021
DOI: 10.6084/m9.figshare.c.5453577.v2, https://osapublishing.figshare.com/collections/A_matrixfree_LevenbergMarquardt_algorithm_forefficient_ptychographic_phase_retrieval/5453577/2
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