Fan-beam Projections Research Articles

Image reconstruction from truncated fan-beam projections along a circular trajectory using the virtual fan-beam method

Objective. In this paper, we investigate how the virtual fan-beam (VFB) method can be used to perform mathematically correct 2D reconstruction in a region-of-interest (ROI), using truncated fan-beam projections acquired on a circular scan, for truncation that only occurs on one side of the object. Approach. We start by choosing a virtual fan-beam trajectory and specifying how to obtain the corresponding virtual projections. Then, three VFB formulas are obtained by applying known super-short-scan (SSS) formulas to this virtual trajectory. Two of them perform the backprojection in a virtual parallel geometry and the third in the virtual fan-beam geometry. Next, we develop two VFB formulas that perform the backprojection step in the fan-beam acquisition geometry. Main results. We present five VFB reconstruction formulas for this truncation setting. To our knowledge, the two VFB formulas performing the backprojection in the fan-beam acquisition geometry are new. Moreover, the five VFB formulas presented here obtain accurate reconstruction in a larger ROI than what has been previously reported in the literature in the same setting. A complete mathematical derivation of these five VFB formulas is given, and their implementation is described step by step. Numerical simulations, using the Forbild head and thorax phantoms, demonstrate the efficacy of these formulas. A spatial resolution analysis and a variance study indicate minor differences between these five VFB formulas. Significance. This work shows that many different VFB formulas can be applied to perform mathematically correct 2D reconstruction in a ROI, in case of truncated fan-beam projections acquired on a circular scan. Moreover, the two new VFB formulas, with backprojection in the acquisition geometry, may open the path for an extension of the VFB method to 3D reconstruction from transversely truncated cone-beam projection acquired on a circular scan.

Separated Fan-Beam Projection with Gaussian Convolution for Invariant and Robust Butterfly Image Retrieval.

Butterfly image retrieval is a challenging issue requiring the feature representation not only to be sensitive to the subtle inter-class difference but also to remain robust to large intra-class variations. Fan-beam projection is a mathematical tool originally applied to computed tomographic (CT) reconstruction of objects. In this paper, we introduce it for the first time into object recognition field. Separated fan-beam projection followed by Gaussian convolutions of different widths are designed to extract multiscale invariant features, patch-projection angles (PPA) and texture-projection angles (TPA), for separately depicting the patch patterns and texture properties of butterfly images. The PPA and TPA are then treated as heterogeneous co-occurrence patterns to be fused by a 2D histograms as final feature representation. We present a comprehensive experimental evaluation including image retrieval at species and subspecies levels, complementarity to deep-learning features, invariance and robustness. All the results consistently show the superior performance of the proposed method over the state-of-the arts.

Cone-beam pair-wise data consistency conditions in helical CT.

Data consistency conditions (DCC) are mathematical equations characterizing the redundancy in X-ray projections. They have been used to correct inconsistent projections before computed tomography (CT) reconstruction. This article investigates DCC for a helical acquisition with a cylindrical detector, the geometry of most diagnostic CT scanners. The acquired projections are analyzed pair-by-pair. The intersection of each plane containing the two source positions with the corresponding cone-beams defines two fan-beams for which a DCC can be computed. Instead of rebinning the two fan-beam projections to a conventional detector, we directly derive the DCC in detector coordinates. If the line defined by two source positions intersects the field-of-view (FOV), the DCC presents a singularity which is accounted for in our numerical implementation to increase the number of DCC compared to previous approaches which excluded these pairs of source positions. Axial truncation of the projections is addressed by identifying for which set of planes containing the two source positions the fan-beams are not truncated. The ability of these DCC to detect breathing motion has been evaluated on simulated and real projections. Our results indicate that the DCC can detect motion if the baseline and the FOV do not intersect. If they do, the inconsistency due to motion is dominated by discretization errors and noise. We therefore propose to normalize the inconsistency by the noise to obtain a noise-aware metric which is mostly sensitive to inconsistencies due to motion. Combined with a moving average to reduce noise, the derived DCC can detect breathing motion.

Fan-beam projection based modulation classification for optical systems with phase noise effect

Fan-beam projection based modulation classification for optical systems with phase noise effect

Hand Gestures Detecting Using Radon And Fan Beam Projection Features

Recognizing hand gestures is one of the most efficient ways of human interaction with a computer and an important field in computer vision and machine learning. This subject matter enables many applications to allow users to communicate the interfaces of different systems, without the need for additional hardware. Therefore, the primary goal of gesture recognition is to create systems in order to identify specific human gestures and use them to transmit information and signals or control various devices. There are more research in the field of pattern recognition especially in gesture recognition .Some of these research focus on dimension reduction , other on recognition model, and in features selection type..etc. In this research, the static hand gesture is detected depending on applying radon features and fan beam projection on hand images to compute the projection by given angles. The reason for adopting these techniques is to take its advantages in giving features not related to the shape and size of the object . The decision tree model is used in recognition stage to detect five different hand gestures , and all the results are reported.

Fan-beam projection for modulation classification in optical wireless communication systems.

The focus of most research nowadays in the field of communication technology is on increasing bandwidth in wireless connectivity. Adaptive modulation can be used to enhance efficiency of communication systems. Adaptive modulation requires modulation format identification (MFI) at the receiver side to avoid the overhead required to determine the modulation type at the receiver. We present an MFI algorithm based on fan-beam projection to generate patterns from the constellation diagrams that are more discriminative. The constellation diagrams are obtained as images for eight different modulation formats (2/4/8/16 - PSK and 8/16/32/64 - QAM). Different classifiers such as AlexNet, VGG16, and VGG19 are studied and compared for the task of MFI. Evaluation of this proposed algorithm is performed by estimating the classification accuracy at different optical signal-to-noise ratios (OSNRs) ranging from 5 to 30 dB. The simulation results reveal that the proposed algorithm succeeds in identifying the wireless optical modulation format blindly with a classification accuracy up to 100% even at low OSNR values less than 8 dB compared with the related work.

Pixel-driven computation of parallel and fan-beam projections of a digital image based on pixel-representation using a new formula

BackgroundThe computation of the projections of a digital image – modelled as a superposition of square pixels – is essential in several algorithms in computed tomography, and also in many machine vision applications. Projections of digital images are computed through the ray-driven approach. Current pixel-driven methods, though simpler, involve interpolation kernels in the projection-domain – not based on the exact Radon transform (RT) of a square. MethodsA new analytical formula – for the line-integral of the unit pixel – simpler than that published previously, is derived. The formula allows easy, pixel-driven computation of the RT of a digital image based on the pixel model i.e., Riemann-sum approximation to the line integral. The method naturally allows pixel-driven backprojection, based on the same (pixel) model. The approach is extended to computing projections over divergent (fan-) beams, and its application as a generalized version of the traditional Hough transform, is discussed. ResultsThe Radon transform of the unit-pixel match that of a digital square image. The RT, of a mathematical phantom consisting of a superposition of elliptical disks, compares well with that based on analytical formula. A comparative study with the pixel driven approach with interpolation in the projection-domain, and its important variant, is included. The fan-beam projections of the square image and the phantom are presented. The applicability of the RT in estimating the Hough transform over precise lines, is shown. ConclusionThe new formula, a simplified version of that of Deans, is useful in pixel-driven computation of parallel and fan-beam projections based on Riemann-sum approximation, which is exact in the case of the common pixel-based image model. Pixel-driven approach is amenable to parallel, and also region-of-interest computation. The method is useful in CT as well as machine vision applications.

Fan-beam Projection-based Feature Extraction for Facial Expression Recognition

This paper presents a novel method of feature extraction using Fan beam projection-based data. The Fanbeam projection covers the image completely and hence gathers all the important information. Even though the image quality is distorted, this type of feature extraction method helps to gather all the important information as there is a huge volume of projection data. Also, the use of multiple detectors speeds up the entire process. All the projections of the image together form a sinogram image which is unique for each facial expression image. Hence, the sinogram image is divided into grids and the histogram formation results in a feature vector for each image. The classification of these feature vectors using Radial Basis Function-based Extreme learning Machine (RBF-ELM) results in high classification accuracy for all the datasets.

Accuracy and Reliability of Standing Lateral Lumbar Radiographs for Measurements of Spinopelvic Parameters.

Retrospective observational study. To assess the accuracy and reliability of standing lateral lumbar radiographs for measurements of spinopelvic parameters, compared with whole-spine EOS® images. Lateral lumbar radiographs are commonly used for measurements of spinopelvic parameters. However, variable magnifications by fan-beam x-ray projection at margins may cause measurement errors. Fifty consecutive patients with standing lateral lumbar radiographs and whole-spine EOS® images were retrospectively reviewed from March to July in 2019. Two orthopedic surgeons (observers) independently measured the spinopelvic parameters including pelvic incidence (PI), pelvic tilt (PT), sacral slope (SS), and lumbar lordosis (LL) on the computers. These spinopelvic parameters of each patient were measured twice on both lateral lumbar radiograph and EOS® image by two observers with the usage of Surgimap software. The measurement difference and agreement of each parameter value between lateral lumbar radiographs and EOS® images were analyzed by paired t test and the interclass correlation coefficient (ICC) respectively. Intra- and inter-observer's reliabilities of both imaging methods were assessed by ICC. The measurement difference of each spinopelvic parameter on EOS® images and lateral lumbar radiographs was less than 1° on average. Only the measurement difference of PI value revealed statistically significant (P = 0.020) with 0.9° discrepancy (95% confidential interval: 0.2-1.6), which indicated no clinical significance. The ICC values of lateral lumbar radiographs and EOS® images were more than 0.870 (range, 0.872-0.976), thus showed good to excellent measurement agreement between both imaging methods. All the ICC values for evaluating intra- and inter-observer reliability were greater than 0.960 (range, 0.963-0.993), indicating excellent reliability for observer's measurements. Measurements of spinopelvic parameters (PI, PT, SS, and LL) on standing lateral lumbar radiographs are accurate and reliable, which are comparable to whole-spine EOS® images.Level of Evidence: 3.

Region-Based Segmentation and Wiener Pilot-Based Novel Amoeba Denoising Scheme for CT Imaging.

Computed tomography (CT) is one of the most common and beneficial medical imaging schemes, but the associated high radiation dose injurious to the patient is always a concern. Therefore, postprocessing-based enhancement of a CT reconstructed image acquired using a reduced dose is an active research area. Amoeba- (or spatially variant kernel-) based filtering is a strong candidate scheme for postprocessing of the CT image, which adapts its shape according to the image contents. In the reported research work, the amoeba filtering is customized for postprocessing of CT images acquired at a reduced X-ray dose. The proposed scheme modifies both the pilot image formation and amoeba shaping mechanism of the conventional amoeba implementation. The proposed scheme uses a Wiener filter-based pilot image, while region-based segmentation is used for amoeba shaping instead of the conventional amoeba distance-based approach. The merits of the proposed scheme include being more suitable for CT images because of the similar region-based and symmetric nature of the human body anatomy, image smoothing without compromising on the edge details, and being adaptive in nature and more robust to noise. The performance of the proposed amoeba scheme is compared to the traditional amoeba kernel in the image denoising application for CT images using filtered back projection (FBP) on sparse-view projections. The scheme is supported by computer simulations using fan-beam projections of clinically reconstructed and simulated head CT phantoms. The scheme is tested using multiple image quality matrices, in the presence of additive projection noise. The scheme implementation significantly improves the image quality visually and statistically, providing better contrast and image smoothing without compromising on edge details. Promising results indicate the efficacy of the proposed scheme.

A dual-domain deep learning-based reconstruction method for fully 3D sparse data helical CT

Helical CT has been widely used in clinical diagnosis. In this work, we focus on a new prototype of helical CT, equipped with sparsely spaced multidetector and multi-slit collimator (MSC) in the axis direction. This type of system can not only lower radiation dose, and suppress scattering by MSC, but also cuts down the manufacturing cost of the detector. The major problem to overcome with such a system, however, is that of insufficient data for reconstruction. Hence, we propose a deep learning-based function optimization method for this ill-posed inverse problem. By incorporating a Radon inverse operator, and disentangling each slice, we significantly simplify the complexity of our network for 3D reconstruction. The network is composed of three subnetworks. Firstly, a convolutional neural network (CNN) in the projection domain is constructed to estimate missing projection data, and to convert helical projection data to 2D fan-beam projection data. This is follwed by the deployment of an analytical linear operator to transfer the data from the projection domain to the image domain. Finally, an additional CNN in the image domain is added for further image refinement. These three steps work collectively, and can be trained end to end. The overall network is trained on a simulated CT dataset based on eight patients from the American Association of Physicists in Medicine (AAPM) Low Dose CT Grand Challenge. We evaluate the trained network on both simulated datasets and clinical datasets. Extensive experimental studies have yielded very encouraging results, based on both visual examination and quantitative evaluation. These results demonstrate the effectiveness of our method and its potential for clinical usage. The proposed method provides us with a new solution for a fully 3D ill-posed problem.

Novel FBP based sparse-view CT reconstruction scheme using self-shaping spatial filter based morphological operations and scaled reprojections

Computed tomography (CT) has been a major contributor in revolutionizing and commercializing the medical imaging industry. However, most of the commonly used CT reconstruction algorithms need sufficiently dense angular sampling views or a substantial dose of hazardous X-ray radiations. Reducing the radiation dose causes degradation in the quality of the reconstructed image, due to additional artifacts. The paper presents a novel algorithm for efficient CT reconstruction from under-sampled projections; which leads to radiation dose reduction with quality image reconstruction. The Sparse-View projection data is enhanced using a series of post-processing algorithms and computer based reprojection. The process involves enhancement through self-shaping/amoeba based morphological spatial filtering. The use of self-shaping spatial filter kernel in the area of under-sampled CT reconstruction is a novel contribution. The scheme is supported by computer simulations using fan-beam projections of clinically reconstructed and simulated head CT phantoms. The proposed scheme is compared with classical reconstruction techniques for reconstruction image quality, accuracy, speed, and robustness in the presence of noise. Promising results indicate the efficacy of proposed scheme. An efficient scheme for image enhancement of Sparse-View CT is presented. The results demonstrate that the proposed scheme is visually and statistically better than classical CT reconstruction techniques, as evaluated using various image quality matrices. The presented scheme is more robust to noise in CT projections and effective for enhancing few-views reconstruction.

View-driven compressed sensing method of CT image reconstruction

In order to significantly reducing the X-ray dose of CT examination, this study focuses on reconstructing the tomographic images from sparse projection data with sufficient accuracy. Aiming at two-dimensional (2D) image reconstruction of fan-beam projection under circular scanning, this paper proposes the view-driven system model and designs a CT iterative image reconstruction method by combining the iterative algorithm and the compressed sensing theory. The simulation results show that the algorithm has high numerical accuracy, low computational complexity, less memory overhead, and strong engineering practicability under the condition of ultra-sparse projection data (no more than 20 view angles for fan-beam scanning in the range of [0,2π)).

Coded Aperture Optimization in X-Ray Tomography via Sparse Principal Component Analysis

Coded aperture X-ray computed tomography (CAXCT) systems reconstruct high quality images of the inner structure of an object from a few coded illumination measurements. Since the computed tomography (CT) system matrix is highly structured, random coded apertures lead to lower quality image reconstructions. In this paper, the noisy forward models of CAXCT in both Gaussian noise and Poisson noise are formulated and analyzed. In addition, a coded aperture optimization approach based on sparse principal component analysis is proposed to maximize the information sensed by a set of fan-beam projections. The complexity of the proposed optimization method is on the same order of magnitude as that of state-of-the-art methods but provide superior image quality. Computational experiments using simulated datasets and real datasets show gains up to $\sim$ 4.3 dB with SNR = 25 dB in the reconstruction image quality compared with that attained by random coded apertures.

Planar Imaging of Stagnant and Hydrodynamic Fluid using Miniaturized ECT Device

This paper discusses the development of an on chip planar capacitance tomography (ECT) for stagnant and hydrodynamic multiphase fluid monitoring. The 8-electrode planar ECT device is developed based on Lab-on-chip (LOC) or microfluidic device concept. The ECT with LOC application is an improved design to allow ECT to be portable and small scaled measurement. To reconstruct images, ECT measures the permittivity variation within the sensing area. Eight-planar electrodes with dimension of 5.00 mm × 2.08 mm (length × width) are fabricated on printed circuit board (PCB). These electrodes are aligned to circulate 16 mm diameter of sensing area. For stagnant sample, the design of the chamber is simpler from the hydrodynamic flow. The hydrodynamic flow consists with two inlets to allow multiphase flow testing. Fan beam projection technique is utilized with Linear Back Projection (LBP) algorithm to reconstruct images of the substance within the chamber. Time is an important item for hydrodynamic flow compared to stagnant sample to ensure that the data taken is useful to the user. For stagnant experiment, the ECT system able to produce image reconstruction for water – air, oil – water and yeast – glucose samples. For hydrodynamic flow, the test conducted for immiscible water – oil sample, and miscible water – glucose solution is done. The results show the system produce the best result when one liquid is dominating the sensing area.

Geometry and energy constrained projection extension.

In clinical computed tomography (CT) applications, when a patient is obese or improperly positioned, the final tomographic scan is often partially truncated. Images directly reconstructed by the conventional reconstruction algorithms suffer from severe cupping and direct current bias artifacts. Moreover, the current methods for projection extension have limitations that preclude incorporation from clinical workflows, such as prohibitive computational time for iterative reconstruction, extra radiation dose, hardware modification, etc.METHOD:In this study, we first established a geometrical constraint and estimated the patient habitus using a modified scout configuration. Then, we established an energy constraint using the integral invariance of fan-beam projections. Two constraints were extracted from the existing CT scan process with minimal modification to the clinical workflows. Finally, we developed a novel dual-constraint based optimization model that can be rapidly solved for projection extrapolation and accurate local reconstruction. Both numerical phantom and realistic patient image simulations were performed, and the results confirmed the effectiveness of our proposed approach. We establish a dual-constraint-based optimization model and correspondingly develop an accurate extrapolation method for partially truncated projections. The proposed method can be readily integrated into the clinical workflow and efficiently solved by using a one-dimensional optimization algorithm. Moreover, it is robust for noisy cases with various truncations and can be further accelerated by GPU based parallel computing.

Sparse 3D Radon Space Rigid Registration of CT Scans: Method and Validation Study.

We present a new method for rigid registration of CT datasets in 3D Radon space based on sparse sampling of scanning projections. The inputs are the two 3D Radon transforms of the CT scans, one densely sampled and the other sparsely sampled (limited number of scan angles/ranges). The output is the rigid transformation that best matches them. The method first finds the best matching between each projection direction vector in the sparse transform and the corresponding direction vector in the dense transform. It then solves a system of linear equations derived from the direction vector pairs (parallel-beam projections) or finds a solution by non-linear optimization (fan-beam and cone-beam projections). Experimental studies show that our method for 3D parallel beam registration outperforms image space registration in terms of convergence range with significantly reduced X-ray dose compared to a full conventional CT scan.

ANALYSIS ON THE PERFORMANCE OF LED AND LASER DIODE WITH CHARGE COUPLED DEVICE (CCD) LINEAR SENSOR MEASURING DIAMETER OF OBJECT

Simple experiment measuring diameter of a solid object (coin) using LED and laser diode with Charge Coupled Device (CCD) linear sensor was conducted in this early stage study. Mostly, CCD and laser diode system are higher in cost because CCD used in industries equipped with an anti blooming protection system to protect the CCD pixel from receiving too high laser light intensities. Low cost atomic laser (Helium: Neon 10:1) with simple modification on light propagation is introduced. Combination of fan beam and parallel beam projection helps to reduce light intensities and expand laser light coverage area. Statistical analyses based on dot plot graph, Anderson Darling test and T-test were applied to choose the best transmitter for Charge Coupled Device (CCD) sensor. Based on T-test results with 95% confidence interval, low intensity laser diode for 5 and 10 cent diameter measurement gave P-value greater than 0.05, accepts laser as the best transmitter compared to LED. Single sensor data for LED and laser used for image reconstruction as an additional approach to prove the above result.

Data consistency conditions for truncated fanbeam and parallel projections.

In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction. These DCCs take the form of polynomial expressions for a weighted backprojection of the projections. The purpose of this work was to present the new DCCs for truncated parallel projections, to extend these conditions to truncated fanbeam projections on a circular trajectory, to verify the conditions with numerical examples, and to present a model of how DCCs could be applied with a toy problem in patient motion estimation with truncated projections. A mathematical derivation of the new parallel DCCs was performed by substituting the underlying imaging equation into the mathematical expression for the weighted backprojection and demonstrating the resulting polynomial form. This DCC result was extended to fanbeam projections by a substitution of parallel to fanbeam variables. Ideal fanbeam projections of a simple mathematical phantom were simulated and the DCCs for these projections were evaluated by fitting polynomials to the weighted backprojection. For the motion estimation problem, a parametrized motion was simulated using a dynamic version of the mathematical phantom, and both noiseless and noisy fanbeam projections were simulated for a full circular trajectory. The fanbeam DCCs were applied to extract the motion parameters, which allowed the motion contamination to be removed from the projections. A reconstruction was performed from the corrected projections. The mathematical derivation revealed the anticipated polynomial behavior. The conversion to fanbeam variables led to a straight-forward weighted fanbeam backprojection which yielded the same function and therefore the same polynomial behavior as occurred in the parallel case. Plots of the numerically calculated DCCs showed polynomial behavior visually indistinguishable from the fitted polynomials. For the motion estimation problem, the motion parameters were satisfactorily recovered and ten times more accurately for the noise-free case. The reconstructed images showed that only a faint trace of the motion blur was still visible after correction from the noisy motion-contaminated projections. New DCCs have been established for fanbeam and parallel projections, and these conditions have been validated using numerical experiments with truncated projections. It has been shown how these DCCs could be applied to extract parameters of unwanted physical effects in tomographic imaging, even with truncated projections.

Optimal beam arrangement design for two-dimensional temperature and concentration reconstruction using ASA and SQP algorithms

Laser absorption spectroscopy was combined with an algebraic iterate algorithm to optimize beam arrangement for temperature and concentration reconstruction. A sequential quadratic programming algorithm (SQP) based on the adaptive simulated annealing algorithm (ASA) was added to improve computational efficiency and obtain an optimized optical layout. Numerical results show that temperature and concentration reconstructed using the optimized beam arrangement have normalized absolute errors of 2.08% and 0.94%. The optimal beam array design reconstructs images effectively compared with parallel- and fan-beam projection given the same number of projections. The beam optimization strategy can provide the experimental design heuristics.