The Mathematical Foundations of 3D Compton Scatter Emission Imaging

The mathematical principles of tomographic imaging using detected (unscattered) X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transform has been introduced recently to support imaging principles of collimated detector systems. The second class is new and is closely related to the Compton camera imaging principles and invertible under special conditions. As they are poised to play a major role in future designs of biomedical imaging systems, we present an account of their most important properties which may be relevant for active researchers in the field

Scattered Radiation Emission Imaging: Principles and Applications

Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields

Detecting small low emission radiating sources

The article addresses the possibility of robust detection of geometrically small, low emission sources on a significantly stronger background. This problem is important for homeland security. A technique of detecting such sources using Compton type cameras is developed, which is shown on numerical examples to have high sensitivity and specificity and also allows to assign confidence probabilities of the detection. 2D case is considered in detail

Quantitative Techniques for PET/CT: A Clinical Assessment of the Impact of PSF and TOF

Tomographic reconstruction has been a challenge for many imaging applications, and it is particularly problematic for count-limited modalities such as Positron Emission Tomography (PET). Recent advances in PET, including the incorporation of time-of-flight (TOF) information and modeling the variation of the point response across the imaging field (PSF), have resulted in significant improvements in image quality. While the effects of these techniques have been characterized with simulations and mathematical modeling, there has been relatively little work investigating the potential impact of such methods in the clinical setting. The objective of this work is to quantify these techniques in the context of realistic lesion detection and localization tasks for a medical environment. Mathematical observers are used to first identify optimal reconstruction parameters and then later to evaluate the performance of the reconstructions. The effect on the reconstruction algorithms is then evaluated for various patient sizes and imaging conditions. The findings for the mathematical observers are compared to, and validated by, the performance of three experienced nuclear medicine physicians completing the same task

Varying Collimation for Dark-Field Extraction

Although x-ray imaging is widely used in biomedical applications, biological soft tissues have small density changes, leading to low contrast resolution for attenuation-based x-ray imaging. Over the past years, x-ray small-angle scattering was studied as a new contrast mechanism to enhance subtle structural variation within the soft tissue. In this paper, we present a detection method to extract this type of x-ray scattering data, which are also referred to as dark-field signals. The key idea is to acquire an x-ray projection multiple times with varying collimation before an x-ray detector array. The projection data acquired with a collimator of a sufficiently high collimation aspect ratio contain mainly the primary beam with little scattering, while the data acquired with an appropriately reduced collimation aspect ratio include both the primary beam and small-angle scattering signals. Then, analysis of these corresponding datasets will produce desirable dark-field signals; for example, via digitally subtraction. In the numerical experiments, the feasibility of our dark-field detection technology is demonstrated in Monte Carlo simulation. The results show that the acquired dark field signals can clearly reveal the structural information of tissues in terms of Rayleigh scattering characteristics

SIGNAL AND NOISE CORRELATIONS IN DIAGNOSTIC X-RAY IMAGING DETECTORS

X-ray detectors are an integral part of any x-ray imaging system. In order to maximize system performance, and hence image quality, signal and noise must be efficiently transferred from input to output. Ideally, an x-ray detector should preserve the input signal-to-noise ratio (SNR). However, in reality, various physical processes within the x-ray detector degrade SNR, which consequently results in lower image quality for a given x-ray imaging dose. The goal of this work is to understand how signal and noise correlations limit the performance of diagnostic x-ray detectors, especially those used in high-resolution imaging applications, such as mammography and micro computed tomography (CT). The fundamental spatial resolution and SNR limits caused by signal and noise correlations associated with x-ray interactions was determined using Monte Carlo simulations of the absorbed energy in common x-ray detector materials as a function of incident energy and converter thickness. These fundamental limits help identify potential performance bottlenecks in existing detectors and also serve as target benchmarks for future designs. Theoretical models of signal and noise transfer through the photoelectric effect and CT filtered backprojection algorithm were developed using a cascaded systems analysis to analytically predict how signal and noise correlations affect detector performance and CT image quality, respectively. This work provides x-ray detector manufacturers and imaging scientists (i) a priori knowledge of the fundamental barriers of detector performance, and (ii) “tools” necessary for the design and optimization of radiography and CT based imaging systems. These contributions will not only save time, money and resources, but will ultimately lead to x-ray detectors with higher SNR efficiency, which in turn, may lead to better image quality (greater diagnostic accuracy) and/or lower patient dose (lower cancer risk)

On the V-Line Radon Transform and Its Imaging Applications

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results