A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data

The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images

An algorithm for constrained one-step inversion of spectral CT data

We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.Comment: Submitted to Physics in Medicine and Biolog

Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization

We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TNV leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.Comment: Submitted to Physics in Medicine and Biolog

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

Multi-material spectral photon-counting micro-CT with minimum residual decomposition and self-supervised deep denoising

Spectral micro-CT imaging with direct-detection energy discriminating photon counting detectors having small pixel size (< 100×100 μm2) is mainly hampered by: i) the limited energy resolution of the imaging device due to charge sharing effects and ii) the unavoidable noise amplification in the images resulting from basis material decomposition. In this work, we present a cone-beam micro-CT setup that includes a CdTe photon counting detector implementing a charge summing hardware solution to correct for the charge-sharing issue and an innovative image processing pipeline based on accurate modeling of the spectral response of the imaging system, an improved basis material decomposition (BMD) algorithm named minimum-residual BMD (MR-BMD), and self-supervised deep convolutional denoising. Experimental tomographic projections having a pixel size of 45×45 μm2 of a plastinated mouse sample including I, Ba, and Gd small cuvettes were acquired. Results demonstrate the capability of the combined hardware and software tools to sharply discriminate even between materials having their K-Edge separated by a few keV, such as e.g., I and Ba. By evaluating the quality of the reconstructed decomposed images (water, bone, I, Ba, and Gd), the quantitative performances of the spectral system are here assessed and discusse

Algorithms for enhanced artifact reduction and material recognition in computed tomography

Computed tomography (CT) imaging provides a non-destructive means to examine the interior of an object which is a valuable tool in medical and security applications. The variety of materials seen in the security applications is higher than in the medical applications. Factors such as clutter, presence of dense objects, and closely placed items in a bag or a parcel add to the difficulty of the material recognition in security applications. Metal and dense objects create image artifacts which degrade the image quality and deteriorate the recognition accuracy. Conventional CT machines scan the object using single source or dual source spectra and reconstruct the effective linear attenuation coefficient of voxels in the image which may not provide the sufficient information to identify the occupying materials. In this dissertation, we provide algorithmic solutions to enhance CT material recognition. We provide a set of algorithms to accommodate different classes of CT machines. First, we provide a metal artifact reduction algorithm for conventional CT machines which perform the measurements using single X-ray source spectrum. Compared to previous methods, our algorithm is robust to severe metal artifacts and accurately reconstructs the regions that are in proximity to metal. Second, we propose a novel joint segmentation and classification algorithm for dual-energy CT machines which extends prior work to capture spatial correlation in material X-ray attenuation properties. We show that the classification performance of our method surpasses the prior work's result. Third, we propose a new framework for reconstruction and classification using a new class of CT machines known as spectral CT which has been recently developed. Spectral CT uses multiple energy windows to scan the object, thus it captures data across higher energy dimensions per detector. Our reconstruction algorithm extracts essential features from the measured data by using spectral decomposition. We explore the effect of using different transforms in performing the measurement decomposition and we develop a new basis transform which encapsulates the sufficient information of the data and provides high classification accuracy. Furthermore, we extend our framework to perform the task of explosive detection. We show that our framework achieves high detection accuracy and it is robust to noise and variations. Lastly, we propose a combined algorithm for spectral CT, which jointly reconstructs images and labels each region in the image. We offer a tractable optimization method to solve the proposed discrete tomography problem. We show that our method outperforms the prior work in terms of both reconstruction quality and classification accuracy

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

No-reference evaluation of the reconstructed images in single-shot K-Edge Subtraction X-ray Computed Tomography

Single-shot K-Edge Subtraction X-ray Computed Tomography (CT) with a multi-threshold photon-counting detector is an interesting approach to favour low-dose analyses of a known contrast agent with promising applications in vivo. To assess the minimum detectable concentration of the contrast agent and to favour possible radiation dose reduction and/or faster acquisition time, a significant role is played by the tomographic reconstruction algorithm. By considering experimental images, this work evaluates three CT reconstruction methods and different acquisition statistics via a no-reference assessment of contrast-to-noise ratio and spatial resolution. The results support that, although computationally expensive, a SART-TV reconstruction approach yields adequate results even when a limited number of projections is available