Regularized Multigrid Optimization for Material Reconstruction from Single Medical X-ray Images

Abstract

This thesis presents a novel technique for the estimation of 3D structural and material composition of anatomies imaged with X-rays. These estimates are produced from a single image with associated X-ray detector data. This method is made possible with access to software for X-ray simulation and segmentation, both developed by and provided to us by IBEX Innovations. This work combines existing concepts from optimization and multi-grid methods to present a novel concept for using domain knowledge to sufficiently constrain an otherwise unsolvable problem to produce valuable output. Specifically, it is shown that by transforming knowledge about the shape and composition of anatomies into regularizing functions, we can produce models of their internal structure that are accurate enough to simulate X-ray scatter, and thereby remove noise from the final images in a physics-guided way. By introducing weighted penalties for results that do not conform to expectations from domain knowledge, which are informed by IBEX’s neural network for X-ray segmentation, we can estimate the shape and material composition of a 3D object from a single image which - in theory - does not contain enough information to produce such a model. This work makes use of an X-ray simulation tool and associated data created by IBEX innovations and provided to us. We have created an optimization algorithm that iteratively processes this data with the IBEX simulation tool, then updates the estimated material composition of the imaged anatomy by imposing regularizing functions that penalize models that do not conform to our expectations about real anatomies. This is implemented on multi-grid, showing improved reconstruction quality and speed by producing coarse models first, followed by a custom algorithm for optimally selecting coarsening and refining of the model to produce the most accurate model. By using IBEX’s simulation algorithm, we show that we can constrain an otherwise ill-posed problem. These novel tools allow us to solve the problem of estimating 3D material composition from a single image, by considering simple features of organic shapes such as continuity and smoothness. We demonstrate that with access to sufficiently powerful simulation tools, even simple assumptions about our target facilitate intuitive material estimations. The algorithm presented in this thesis has certain limitations. We are only able to produce models of anatomies at low resolutions, constructed of just two distinct materials, without fully capturing the 3D structure of the anatomy. Nonetheless, we demonstrate that it is possible to capture enough structural information to produce an accurate scatter estimate, which would not be possible without the research we present here. These limitations are imposed to simplify our solutions such that they can be found using conventional hardware, and to constrain our problem into the scope of feasibility. Furthermore, the choice to limit our models to 2.5D and just two materials reflects the models used by IBEX Innovations and their X-ray simulation method, which we require for our optimization. To our understanding, no other published work in this field has applied an approach like ours to X-ray image reconstruction. Inferring from a single image not just depth information, but also an abstraction of information about the internal structure, in a way that is physically motivated. We hope that this concept could be applied to other problems in future, where systems are well understood but hindered by limited data availability or high capture costs.