Analytical Methods and Deep Priors on X-ray Ptychography, Computed Tomography, and Computed Laminography

Barutcu, Semih

doi:https://doi.org/10.21985/n2-az0b-6w68

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Analytical Methods and Deep Priors on X-ray Ptychography, Computed Tomography, and Computed Laminography

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X-ray imaging at nano and micro-scale is of great importance for the material science and defense industry. Large penetration depth and low wavelength of x-rays offer an important potential to image objects at high resolution and in a non-invasive process. While the ever-growing community is pursuing novel applications and looking for improvements in techniques with higher spatial resolution and lower time for imaging processes, there are still facets of x-ray imaging techniques that merit further investigation. This dissertation will describe a few such directions by proposing solutions using analytical methods and deep priors. Chapter 2 analyzes the sequential application of two x-ray imaging methods, x-ray ptychography and computed tomography, and suggests a solution to the combined three-dimensional inverse problem by providing an iterative analytical approach. In Chapter 3, the requirement for the high overlap between successive scanning areas in ptychography is investigated. Applying a combination of different prior knowledge about the scanned object and the x-ray beam shows that the overlap requirement can be relaxed for a target resolution. Chapter 4 provides a solution to the imperfections in the ptychography scanning setup. By utilizing the advantages of automatic differentiation, position errors in the experiments can be corrected for increased reconstruction quality. Chapter 5 addresses the artifacts in reconstructions caused by missing projection angles in the computed tomography setup. We show that deep image priors can be utilized to reduce the artifacts in limited-angle computed tomography. The proposed neural network takes the physical constraints of the forward model into account and takes advantage of the alternating direction method of multipliers structure. While improving the reconstruction quality significantly, it is shown that the method can handle some extreme cases. In Chapter 6, a similar application of deep image priors on computed laminography is shown. Inherent missing information in the laminography setup allows the previous method to be easily adapted to provide a solution leading to increased reconstruction quality. In Chapter 7, deep image priors are combined with deep generative priors to reduce or remove the overlap constraint in ptychography. A pre-trained neural network is optimized with additional priors to have successful reconstructions with no overlap among neighboring scanning areas, which traditional methods require. Chapter 8 shows that the reconstruction resolution for no-overlap data in ptychography can be further improved by combining the previously proposed method with a traditional method using deep oversampling. Usage of oversampling leads to a method having improved reconstruction quality in local regions while maintaining a high resolution and a low acquisition time.

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