Abstract
We introduce the application of maximum-likelihood (ML) principles to the image reconstruction problem in coherent diffractive imaging. We describe an implementation of the optimization procedure for ptychography, using conjugate gradients and including preconditioning strategies, regularization and typical modifications of the statistical noise model. The optimization principle is compared to a difference map reconstruction algorithm. With simulated data important improvements are observed, as measured by a strong increase in the signal-to-noise ratio. Significant gains in resolution and sensitivity are also demonstrated in the ML refinement of a reconstruction from experimental x-ray data. The immediate consequence of our results is the possible reduction of exposure, or dose, by up to an order of magnitude for a reconstruction quality similar to iterative algorithms currently in use.
Highlights
We introduce the application of maximum-likelihood (ML) principles to the image reconstruction problem in coherent diffractive imaging
While the general concepts are meant to apply to CDI at large, we concentrate most of the developments and demonstrations to ptychography
The approach is known to give good results for ptychography. It was shown in [14] that ptychography can be stated as a phase retrieval problem with transverse translation diversity and that gradient-based minimization approaches are surprisingly well behaved for this case, even for essentially one-dimensional (1D) problems [15, 16]
Summary
We introduce the application of maximum-likelihood (ML) principles to the image reconstruction problem in coherent diffractive imaging. While the general concepts are meant to apply to CDI at large, we concentrate most of the developments and demonstrations to ptychography. It was shown in [14] that ptychography can be stated as a phase retrieval problem with transverse translation diversity and that gradient-based minimization approaches are surprisingly well behaved for this case, even for essentially one-dimensional (1D) problems [15, 16] This behaviour was observed in other reconstruction problems where sufficient diversity of measurement is attainable, for instance when repeated measurements can be taken at different known configurations of an optical setup [17,18,19]. Our findings indicate that the best strategy for ptychographic reconstructions is to obtain a first result estimate using the difference map, thereby utilizing its ability to search efficiently the solution space, and follow it by an ML refinement to account for the statistical nature of the data on the final solution
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