Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers
arXiv:1808.05802 · doi:10.1137/18M1188446
Abstract
Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A ptychographyic reconstruction is normally formulated as a blind phase retrieval problem, where both the image (sample) and the probe (illumination) have to be recovered from phaseless measured data. In this article we address a nonlinear least squares model for the blind ptychography problem with constraints on the image and the probe by maximum likelihood estimation of the Poisson noise model. We formulate a variant model that incorporates the information of phaseless measurements of the probe to eliminate possible artifacts. Next, we propose a generalized alternating direction method of multipliers designed for the proposed nonconvex models with convergence guarantee under mild conditions, where their subproblems can be solved by fast element-wise operations. Numerically, the proposed algorithm outperforms state-of-the-art algorithms in both speed and image quality.
arXiv comment23 pages
References in corpus (8)
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Cited by in corpus (8)
- The Numerics of Phase Retrieval
- Advanced Denoising for X-ray Ptychography
- Ptychographic phase-retrieval by proximal algorithms
- Inverse Multislice Ptychography by Layer-wise Optimisation and Sparse Matrix Decomposition
- Dose-efficient Automatic Differentiation for Ptychographic Reconstruction
- Well conditioned ptychograpic imaging via lost subspace completion
- Iterative Joint Ptychography-Tomography with Total Variation Regularization
- Iterative X-ray Spectroscopic Ptychography