Fast Iterative Reconstruction for Multi-spectral CT by a Schmidt Orthogonal Modification Algorithm (SOMA)

Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process of obtaining MSCT data can be modeled as nonlinear equations and the basis material decomposition comes down to the inverse problem of the nonlinear equations. For different spectra data, geometric inconsistent parameters cause geometrical inconsistent rays, which will lead to mismatched nonlinear equations. How to solve the mismatched nonlinear equations accurately and quickly is a hot issue. This paper proposes a general iterative method to invert the mismatched nonlinear equations and develops Schmidt orthogonalization to accelerate convergence. The validity of the proposed method is verified by MSCT basis material decomposition experiments. The results show that the proposed method can decompose the basis material images accurately and improve the convergence speed greatly

First order algorithms in variational image processing

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure

Reconstruction algorithms for multispectral diffraction imaging

Thesis (Ph.D.)--Boston UniversityIn 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