Sparse sampling in X-ray computed tomography via spatial and spectral coded illumination
Date
2020
Authors
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Publisher
University of Delaware
Abstract
The rapid increase in radiation dose by the expanded use of computed tomography (CT) worldwide has led to concerns about future public health problems. Reducing radiation dosage per CT scan, and therefore the risks, has motivated major efforts to develop new approaches for attaining clinically useful images with the lowest possible radiation dose. Multiple approaches used to attain this goal result in a set of incomplete measurements compared to the conventional number of sampling points needed for reconstruction. Incomplete measurements in X-ray transmission CT have been a topic of study for many years in the context of limited angle tomography, where the number of views is reduced considerably. Yet, as demonstrated by multiple research groups, using structured illumination to subsample the detectors instead of the number of angles results in higher quality reconstructions. In the first part of this dissertation, we study the concepts of structured X-ray illumination in the space domain. First, we consider the coded aperture compressive X-ray CT architecture which places a coded aperture in front of an X-ray source to obtain patterned projections; and uses compressive sensing (CS) reconstruction algorithms to recover the image. Coded apertures are filtering masks composed of elements that block or un-block the X-rays in a particular pattern. Given that conventional random coded apertures do not take into account the structure of the sensing matrix, we propose a coded aperture optimization framework based on the point spread function (PSF) of the system, which is used as a measure of the sensing matrix quality. Secondly, we propose a radical modification to the system by using a single-static coded aperture to create structured X-ray bundles in a system coined StaticCode-CT. Furthermore, instead of using conventional CS algorithms for reconstruction, we develop a measurement estimation algorithm that exploits low-rank tensor priors and data-driven deep-learning regularization to synthesize a full set of cone-beam measurements. Then, we use conventional CT reconstruction algorithms to solve the inverse problem. ☐ The reconstructions obtained using conventional CT, contain useful information regarding the morphological structure of the inspected objects. However, for some applications, these gray-scale images are often insufficient for accurate material identification. Spectral CT allows for material characterization in 3D images, a feature not possible with conventional X-ray inspection systems. Currently, photon-counting detectors are used to attain material identification; however, these detectors are costly and have a low spectral resolution which decreases the material identification accuracy. The second part of this dissertation introduces multiple sparse sampling strategies for spectral CT that ameliorate the aforementioned limitations. First, we introduce a new approach referred to as compressive spectral X-ray imaging (CSXI). It extends the concepts of spatial coded illumination to the spectral domain using 3-D coded apertures, which can block, unblock, and attenuate X-rays. Furthermore, it uses an alternating direction method of multipliers (ADMM) to reconstruct the spectral datacube. Subsequently, as an alternative implementation, we combine the proposed StaticCode-CT spatial sampling with dual-energy architectures, which creates an incomplete 4-way tensor with multiple energy intensities as the 4th dimension. Then, we extend our reconstruction algorithms by exploiting the additional joint low-rank and sparse representation of the measurement data. ☐ Throughout this dissertation, we validate, theoretically, and experimentally that the proposed methods offer significant gains over current sparse-sampling methods in terms of reconstruction quality and hardware simplicity. These methods are general, simple to use, and can be easily extended to other imaging systems such as hyperspectral imaging, as well as other CT scanner geometries such as tomosynthesis, and spiral X-ray CT.
Description
Keywords
Coded apertures, Compressive sensing, Computed tomography, Spectral CT, Tensor completion, X-ray