Reconstruction algorithms for multispectral diffraction imaging

Abstract

In conventional Computed Tomography (CT) systems, a single X-ray source spectrum is used to radiate an object and the total transmitted intensity is measured to construct the spatial linear attenuation coefficient (LAC) distribution. Such scalar information is adequate for visualization of interior physical structures, but additional dimensions would be useful to characterize the nature of the structures. By imaging using broadband radiation and collecting energy-sensitive measurement information, one can generate images of additional energy-dependent properties that can be used to characterize the nature of specific areas in the object of interest. In this thesis, we explore novel imaging modalities that use broadband sources and energy-sensitive detection to generate images of energy-dependent properties of a region, with the objective of providing high quality information for material component identification. We explore two classes of imaging problems: 1) excitation using broad spectrum sub-millimeter radiation in the Terahertz regime and measure- ment of the diffracted Terahertz (THz) field to construct the spatial distribution of complex refractive index at multiple frequencies; 2) excitation using broad spectrum X-ray sources and measurement of coherent scatter radiation to image the spatial distribution of coherent-scatter form factors. For these modalities, we extend approaches developed for multimodal imaging and propose new reconstruction algorithms that impose regularization structure such as common object boundaries across reconstructed regions at different frequencies. We also explore reconstruction techniques that incorporate prior knowledge in the form of spectral parametrization, sparse representations over redundant dictionaries and explore the advantage and disadvantages of these techniques in terms of image quality and potential for accurate material characterization. We use the proposed reconstruction techniques to explore alternative architectures with reduced scanning time and increased signal-to-noise ratio, including THz diffraction tomography, limited angle X-ray diffraction tomography and the use of coded aperture masks. Numerical experiments and Monte Carlo simulations were conducted to compare performances of the developed methods, and validate the studied architectures as viable options for imaging of energy-dependent properties.