Numerical and theoretical explorations in helical and fan-beam tomography
نویسندگان
چکیده
Katsevich’s inversion formula for helical tomography is explored in the limit of vanishing pitch, yielding a general reconstruction formula for fan-beam tomography. The relationship of this formula to other formulas in the literature is explored and a rigorous proof of a rebinning formula relating parallel-beam and fan-beam tomography is given. For the case of curved detector coordinates several numerical implementations of this formula and a related fan-beam formula are proposed, numerically implemented, and compared with the standard fan-beam algorithm. This gives insight into some numerical questions also encountered in the three-dimensional case, including a theoretical explanation of the usefulness of a shift in the convolution kernel for removal of ringing artifacts. A new discretization scheme for the derivatives is suggested and shown to be promising in both two and three dimensions. Numerical experiments with simulated as well as real data are presented.
منابع مشابه
Usability assessment of cone beam computed tomography with a full-fan mode bowtie filter compared to that with a half-fan mode bowtie filter
Background: In intensity modulated radiation therapy, cone beam computed tomography (CT) has been used to evaluate patients prior to treatment. This study conducted a comparative evaluation of the image reconstruction ability of the clinically used half-fan bowtie filter and the full-fan bowtie filter. Materals and Methods: A CT simulation marker was inserted inside a human phantom, and the pel...
متن کاملRegions of Backprojection and Comet Tail Artifacts for Pi-Line Reconstruction Formulas in Tomography
We explore two characteristic features of x-ray computed tomography inversion formulas in two and three dimensions that are dependent on π-lines. In such formulas the data from a given source position contribute only to the reconstruction of f(x) for x in a certain region, called the region of backprojection. The second characteristic is a certain small artifact in the reconstruction, called a ...
متن کاملExact and approximate algorithms for helical cone-beam CT.
This paper concerns image reconstruction for helical x-ray transmission tomography (CT) with multi-row detectors. We introduce two approximate cone-beam (CB) filtered-backprojection (FBP) algorithms of the Feldkamp type, obtained by extending to three dimensions (3D) two recently proposed exact FBP algorithms for 2D fan-beam reconstruction. The new algorithms are similar to the standard Feldkam...
متن کاملFast System Matrix Calculation in CT Iterative Reconstruction
Introduction: Iterative reconstruction techniques provide better image quality and have the potential for reconstructions with lower imaging dose than classical methods in computed tomography (CT). However, the computational speed is major concern for these iterative techniques. The system matrix calculation during the forward- and back projection is one of the most time- cons...
متن کاملValidation of computed tomography-based attenuation correction of deviation between theoretical and actual values for four computed tomography scanners
Objective: In this study, we aimed to validate the accuracy of computed tomography-based attenuation correction (CTAC) using the bilinear scaling method.Methods: The measured attenuation coefficient (μm) was compared to a theoretical attenuation coefficient (μt ) using four different CT scanners and an RMI 467 phantom. The effective energy of the CT beam X-rays was calculated, using the aluminu...
متن کامل