Fanbeam Reconstruction Algorithm for Shepp Logan Head Phantom and Histrogram Analysis (original) (raw)
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Image Reconstruction of Computed Tomography Using Fan-Beam Technique
Tomography image reconstruction using fan-beam geometry configuration was studied. The research methodology consisted of a series of experiment using a Matlab image processing toolbox to validate the conceptual framework reconstruction that later might guide the development of application using fan-beam geometry. The Matlab programming knowledge is a vital requirement in the process of developing a software application. Further, the algorithm to create a sinogram from datasets in fan-beam geometry is straightforward and similar to parallel-beam geometry, but the algorithm details to create an image from a sinogram is complex and incomprehensible to novice researchers. The initial procedure involves the process of transforming fan-beam datasets into parallel-beam datasets prior to the image reconstruction process. Literature studies revealed two different methods of datasets organization in tomography acquisition systems which capture the attenuation data of an object. The two methods of data arrangement were row-column and column-row data arrangement. The scope of this study was limited to experimenting with synthetic datasets due to the unavailability of real instrument that implements divergent beam detector at the research facility (Malaysian Nuclear Agency). The research used a convenient way to develop imaging system with Matlab image processing toolbox approach to guide through the development processes of imaging application. This article discusses the knowledge of computed tomography's image reconstruction for divergent beam using back projection by parallel approaches.
Relation between the filtered backprojection algorithm and the backprojection algorithm in CT
IEEE Signal Processing Letters, 2000
In this letter, we present a new fan-beam CT formula, based on which we discuss the relation between the filtered backprojection (FBP) algorithm and the backprojection (BP) algorithm. Specifically, the FBP algorithm can be expressed in a series with its first-order approximation being the BP algorithm. As a result, we identify a link between X-ray CT and number theory.
A differentiable Shepp–Logan phantom and its applications in exact cone-beam CT
Physics in Medicine and Biology, 2005
Recently, several exact cone-beam reconstruction algorithms, such as the generalized filtered-backprojection (FBP) and backprojection-filtration (BPF) methods, have been developed to solve the long object problem. Although the well-known 3D Shepp-Logan phantom (SLP) is often used to validate these algorithms, it is deficient due to the discontinuity of the SLP. In this paper, we first construct a differentiable polynomial function to approximate the unit rectangular function on [−1, 1]. Then, we use this function to obtain a differentiable ellipsoid phantom, whose x-ray transform is differentiable for any smooth scanning trajectory. Finally, we propose a differentiable Shepp-Logan phantom (DSLP) for numerical simulation of the exact cone-beam CT algorithms. Our numerical simulation shows that the reconstructed DSLP has a better image quality than the reconstructed SLP, and is complementary to the traditional SLP for evaluation of the exact cone-beam CT algorithms.
International Journal of Probability and Statistics, 2015
Images of the inside of the human body can be obtained noninvasively using tomographic acquisition and processing techniques. In particular, these techniques are commonly used to obtain X-ray images of the human body. The reconstructed images are obtained given a set of their projections, acquired using reconstruction techniques. A general overview of analytical and iterative methods of reconstruction in computed tomography (CT) is presented in this paper, with a special focus on Back Projection (BP), Filter Back Projection (FBP), Gradient and Bayesian maximum a posteriori (MAP) algorithms. Projections (parallel beam type) for the image reconstruction are calculated analytically by defining two phantoms: Shepp-Logan phantom head model and the standard medical image of abdomen with coverage angle ranging from 0 to 180° with rotational increment of 10°. The original images are grayscale images of size 128 128, 256 256, respectively. The simulated results are compared using quality measurement parameters for various test cases and conclusion is achieved. Through these simulated results, we have demonstrated that the Bayesian (MAP) approach provides the best image quality and appears to be efficient in terms of error reduction.
Image Reconstruction for CT Scanner by Using Filtered Back projection Approach
Image reconstruction in computed tomography (CT) has been extensively studied from different angles, to find new methods and algorithms for better execution of the reconstruction tasks. In this study, three challenging problems in developing a prototype for the image reconstruction system using a summation back projection approach are highlighted namely; blurring effect of the summation back projection computational processes, computational complexity and the necessity for a graphical user interface. Our proposed solutions, which respectively address these problems are to exploit Ram-Lak filter, to utilize a scientific and industrial programming language (FORTRAN) and to use Visual Basic Studio (VB). To examine the solutions, a prototype software has been developed, by which sinograms and slice form of an object's image can be generated. Furthermore, this article presents a comprehensive background study on image reconstruction using filtered back projection (FBP) approaches to develop the CT scanner software application.
Medical Physics, 2006
A novel exact fan-beam image reconstruction formula is presented and validated using both phantom data and clinical data. This algorithm takes the form of the standard ramp filtered backprojection ͑FBP͒ algorithm plus local compensation terms. This algorithm will be referred to as a locally compensated filtered backprojection ͑LCFBP͒. An equal weighting scheme is utilized in this algorithm in order to properly account for redundantly measured projection data. The algorithm has the desirable property of maintaining a mathematically exact result for: the full scan mode ͑2͒, the short scan mode ͑+ full fan angle͒, and the supershort scan mode ͓less than ͑+ full fan angle͔͒. Another desirable feature of this algorithm is that it is derivative-free. This feature is beneficial in preserving the spatial resolution of the reconstructed images. The third feature is that an equal weighting scheme has been utilized in the algorithm, thus the new algorithm has better noise properties than the standard filtered backprojection image reconstruction with a smooth weighting function. Both phantom data and clinical data were utilized to validate the algorithm and demonstrate the superior noise properties of the new algorithm.
Physics in Medicine and Biology, 2005
In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2π angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2π angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm.
International Journal of Biomedical Imaging, 2006
A three-dimensional (3D) weighted helical cone beam filtered backprojection (CB-FBP) algorithm (namely, original 3D weighted helical CB-FBP algorithm) has already been proposed to reconstruct images from the projection data acquired along a helical trajectory in angular ranges up to [0, 2π]. However, an overscan is usually employed in the clinic to reconstruct tomographic images with superior noise characteristics at the most challenging anatomic structures, such as head and spine, extremity imaging, and CT angiography as well. To obtain the most achievable noise characteristics or dose efficiency in a helical overscan, we extended the 3D weighted helical CB-FBP algorithm to handle helical pitches that are smaller than 1 : 1 (namely extended 3D weighted helical CB-FBP algorithm). By decomposing a helical over scan with an angular range of [0, 2π + Δβ] into a union of full scans corresponding to an angular range of [0, 2π], the extended 3D weighted function is a summation of all 3D weighting functions corresponding to each full scan. An experimental evaluation shows that the extended 3D weighted helical CB-FBP algorithm can improve noise characteristics or dose efficiency of the 3D weighted helical CB-FBP algorithm at a helical pitch smaller than 1 : 1, while its reconstruction accuracy and computational efficiency are maintained. It is believed that, such an efficient CB reconstruction algorithm that can provide superior noise characteristics or dose efficiency at low helical pitches may find its extensive applications in CT medical imaging.
Implementation and evaluation of two helical CT reconstruction algorithms in CIVA
2016
The large majority of industrial CT systems reconstruct the 3D volume by using an acquisition on a circular trajec-tory. However, when inspecting long objects which are highly anisotropic, this scanning geometry creates severe artifacts in the reconstruction. For this reason, the use of an advanced CT scanning method like helical data acquisition is an efficient way to address this aspect known as the long-object problem. Recently, several analytically exact and quasiexact inversion formulas for helical cone-beam reconstruction have been proposed. Among them, we identified two algorithms of interest for our case. These algorithms are exact and of filtered back-projection structure. In this work we implemented the filtered-backprojection (FBP) and backprojection-filtration (BPF) algorithms of Zou and Pan (2004). For performance evaluation, we present a numerical comparison of the two selected algorithms with the helical FDK algorithm using both complete (noiseless and noisy) and truncated data generated by CIVA (the simulation platform for non-destructive testing techniques developed at CEA).
Helical CT Reconstruction from Wide Cone-Beam Angle Data Using ART
Brazilian Symposium on Computer Graphics and Image Processing, 2003
We report on new results on the use of Algebraic Reconstruction Techniques (ART) for reconstructing from helical cone-beam Computerized Tomography (CT) data. We investigate two variants of ART for this task: a standard one that considers a single ray in an iterative step and a block version which groups several cone-beam projections when calculating an iterative step. Both algorithms were implemented using modified Kaiser-Bessel window functions, also known as blobs, placed on the body-centered cubic (bcc) grid. The algorithms were used to reconstruct a modified 3D Shepp-Logan phantom from data collected for the PI-geometry for two different maximum cone-beam angles (±9.46 • and ±18.43 • ). Both scattering and quantum noise (for three different noise levels) were introduced to create noisy projections. The results presented here (for both noiseless and noisy data sets) point to the fact that, as opposed to filtered backprojection algorithms, the quality of the reconstructions produced by the ART methods does not suffer from the increase in the cone-beam angle.