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Register a new userJoint fan-beam CT and Compton scattering tomography: analysis and image reconstruction
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Added by
Lorenz Kuger
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The recent development of energy-resolving cameras opens the way to new types of applications and imaging systems. In this work, we consider computerized tomography (CT) with fan beam geometry and equipped with such cameras. The measured radiation is then a function of the positions of the source and detectors and of the energy of the incoming photons. Due to the Compton effect, the variations in energy (or spectrum) of the measurement are modeled in terms of scattering events leading to the so-called Compton scattering tomography (CST). We propose an analysis of the spectral data in terms of modelling and mapping properties which results in a general reconstruction strategy. Thanks to the supplementary information given by the energy, this joint CT-CST scanner makes accurate reconstructions of characteristics of the sought-for object possible for very few source positions and a small number of detectors. The general reconstruction strategy is finally validated on synthetic data via a total variation iterative scheme. We further show how the method can be extended to high energetic polychromatic radiation sources. Also illustrative, this work motivates the potential of combining conventional CT and Compton scattering imaging (CSI) with various architectures in 2D and 3D.
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3D Compton scattering imaging is an upcoming concept exploiting the scattering of photons induced by the electronic structure of the object under study. The so-called Compton scattering rules the collision of particles with electrons and describes their energy loss after scattering. Although physically relevant, multiple-order scattering was so far not considered and therefore, only first-order scattering is generally assumed in the literature. The purpose of this work is to argument why and how a contour reconstruction of the electron density map from scattered measurement composed of first- and second-order scattering is possible (scattering of higher orders is here neglected). After the development of integral representations for the first- and second-order scattering, this is achieved by the study of the smoothness properties of associated Fourier integral operators (FIO). The second-order scattered radiation reveals itself to be structurally smoother than the radiation of first-order indicating that the contours of the electron density are essentially encoded within the first-order part. This opens the way to contour-based reconstruction techniques when using multiple scattered data. Our main results, modeling and reconstruction scheme, are successfully implemented on synthetic and Monte-Carlo data.
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive (or resolving) detectors, and where the X-ray source is polychromatic. We consider the case where the measurements in the dark field are dominated by the Compton scattering process. This leads us to a 2D inverse problem where we aim to reconstruct an electron density slice from its integrals over discs whose boundaries intersect the given source point. We show that a unique solution exists for smooth densities compactly supported on an annulus centred at the source point. Using Sobolev space estimates we determine a measure for the ill posedness of our problem based on the criterion given by Natterer (The mathematics of computerized tomography SIAM 2001). In addition, with a combination of our method and the more common attenuation coefficient reconstruction, we show under certain assumptions that the atomic number of the target is uniquely determined. We test our method on simulated data sets with varying levels of added pseudo random noise.
Low-dose CT image reconstruction has been a popular research topic in recent years. A typical reconstruction method based on post-log measurements is called penalized weighted-least squares (PWLS). Due to the underlying limitations of the post-log statistical model, the PWLS reconstruction quality is often degraded in low-dose scans. This paper investigates a shifted-Poisson (SP) model based likelihood function that uses the pre-log raw measurements that better represents the measurement statistics, together with a data-driven regularizer exploiting a Union of Learned TRAnsforms (SPULTRA). Both the SP induced data-fidelity term and the regularizer in the proposed framework are nonconvex. The proposed SPULTRA algorithm uses quadratic surrogate functions for the SP induced data-fidelity term. Each iteration involves a quadratic subproblem for updating the image, and a sparse coding and clustering subproblem that has a closed-form solution. The SPULTRA algorithm has a similar computational cost per iteration as its recent counterpart PWLS-ULTRA that uses post-log measurements, and it provides better image reconstruction quality than PWLS-ULTRA, especially in low-dose scans.
Here we present a novel microlocal analysis of a new toric section transform which describes a two dimensional image reconstruction problem in Compton scattering tomography and airport baggage screening. By an analysis of two separate limited data problems for the circle transform and using microlocal analysis, we show that the canonical relation of the toric section transform is 2--1. This implies that there are image artefacts in the filtered backprojection reconstruction. We provide explicit expressions for the expected artefacts and demonstrate these by simulations. In addition, we prove injectivity of the forward operator for $L^infty$ functions supported inside the open unit ball. We present reconstructions from simulated data using a discrete approach and several regularizers with varying levels of added pseudo-random noise.
We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem of the Jacobian of the underlying multi-modality or multi-contrast images. Derivation of data fidelity for Jacobian and transformation of noise distribution are also detailed. The new minimization problem yields an optimal $O(1/k^2)$ convergence rate, where $k$ is the iteration number, and the per-iteration cost is low thanks to the close-form matrix-valued shrinkage. We conducted numerical tests on a number multi-contrast magnetic resonance image (MRI) datasets, which show that the proposed method significantly improves reconstruction efficiency and accuracy compared to the state-of-the-arts.
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