Chrysoula Tsogka, University of California Merced
Authors: M. Moscoso, A. Novikov, G. Papanicolaou and C. Tsogka
2023 AWM Research Symposium
Computational Inverse Problems and Uncertainty Quantification [Organized by Julianne Chung, Rosemary Renaut, and Malena Sabate-Landman]

We consider imaging absorbing as well as non-absorbing objects using intensity only measurements. Objects with high absorption contrast can be imaged effectively using multiple illuminations and/or masks as in ghost imaging. On the other hand, transparent objects with low absorption contrast are more challenging to be imaged when only intensities are measured, even when they significantly change the phase of the waves as they go through them. We present a computational imaging approach that allows quantitative imaging of both absorbing and transparent objects. We solve the phase retrieval problem sequentially accounting first only for the incoherent contributions to the data. Then in a second step the coherent contributions are taken into account. This amounts to solving linear problems with unknowns whose size is linear in the number of pixels of the image. This robust dimension reduction is achieved using the Noise Collector to absorb the error that is due to the contribution of the unmodeled unknowns in each step. This problem arises in various fields such as X-ray crystallography, electron microscopy, coherent diffractive imaging and astronomy. The proposed algorithm guarantees exact recovery if the image is sparse with respect to a given basis, and it can be used, without any modification, when the illumination is partially coherent. This is important for, for example, phase-contrast X-ray imaging because fully coherent sources of X-rays are very hard to be obtained.

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