Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm
The phase retrieval problem, where one aims to recover a complex-valued image from far-field 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 closed-form 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 data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square 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 least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton 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 state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order 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 first-order algorithms.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE; National Institutes of Health (NIH); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- Grant/Contract Number:
- AC02-06CH11357; R01 GM104530; R01 MH115265; AC02-76SF00515
- OSTI ID:
- 1806256
- Alternate ID(s):
- OSTI ID: 1813106; OSTI ID: 1814924
- Journal Information:
- Optics Express, Journal Name: Optics Express Vol. 29 Journal Issue: 15; ISSN 1094-4087
- Publisher:
- Optical Society of AmericaCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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