Over recent years, various exact cone-beam reconstruction algorithms have been proposed. The derivations of these algorithms are quite complicated, and often difficult to see the fundamental connections among these methods and their key steps. In this paper, we present a straightforward perspective based on the Fourier transform, which is a universal principle for parallel and divergent beam computed tomography (CT). The formulas in this paper are not only consistent with the latest findings in the field but also valid under more general conditions.
Theoretically, the ramp filter for filter backprojection reconstruction in X-ray computed tomography (CT) is a generalized function, expressed as |ω| in the frequency domain and -1/(2π2t2) in the real space. The traditional method for designing a practical filter is to select a curve in the frequency domain which is close to the function |Οω| in some sense. Similarly, to design a practical filter one also can select a function in the real space which approximates the function -1/(2π2t2). Several approximations are studied, leading to either known or new filters. The image reconstructed using the new filter is comparable with that using the band-limited filter.
KEYWORDS: Sensors, Land mines, General packet radio service, Mining, Hough transforms, Detection and tracking algorithms, Electromagnetic coupling, Ground penetrating radar, Metals, Algorithm development
Ground penetrating radar (GPR) has been proposed as an effective sensing modality for reducing the excessively high false alarm rates often encountered in landmine detection applications. Ground penetrating radar is sensitive to discontinuities in the interrogated medium, rather than the presence of metal, and thus exploits a different phenomenology than electromagnetic induction (EMI) sensors. Thus, unique signals that are dependent on the composition of the targets can be obtained from buried objects. Consequently, the detection of low metal content targets is improved since the radar responds to non-metallic objects, such as wood, plastic, and stone, as well as metallic objects. When the GPR sensor is mounted on a moving platform, the target signatures are hyperbolas in a time-domain data record. Furthermore, the hyperbolas from different targets often exhibit different characteristics. The goal of this work is to develop robust signal processing algorithms which exploit this knowledge to improve target detection and discrimination. Among the algorithms considered are a Bayesian approach and an approach similar to the Hough transform. The algorithms are evaluated using real data collected with fielded GPR sensors, and are compared in terms of their computational requirements as well as their detection and discrimination performance.
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