Implementation of Radon Transformation for Electrical Impedance Tomography (EIT)

BackgroundPositron Emission Tomography (PET), Computed Tomography (CT), PET/CT and Single Photon Emission Tomography (SPECT) are non-invasive imaging tools used for creating two dimensional (2D) cross section images of three dimensional (3D) objects. PET and SPECT have the potential of providing functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules, whereas CT visualizes X-ray density in tissues in the body. PET/CT provides fused images representing both functional and anatomical information with better precision in localization than PET alone.Images generated by these types of techniques are generally noisy, thereby impairing the imaging potential and affecting the precision in quantitative values derived from the images. It is crucial to explore and understand the properties of noise in these imaging techniques. Here we used autocorrelation function (ACF) specifically to describe noise correlation and its non-isotropic behaviour in experimentally generated images of PET, CT, PET/CT and SPECT.MethodsExperiments were performed using phantoms with different shapes. In PET and PET/CT studies, data were acquired in 2D acquisition mode and reconstructed by both analytical filter back projection (FBP) and iterative, ordered subsets expectation maximisation (OSEM) methods. In the PET/CT studies, different magnitudes of X-ray dose in the transmission were employed by using different mA settings for the X-ray tube. In the CT studies, data were acquired using different slice thickness with and without applied dose reduction function and the images were reconstructed by FBP. SPECT studies were performed in 2D, reconstructed using FBP and OSEM, using post 3D filtering. ACF images were generated from the primary images, and profiles across the ACF images were used to describe the noise correlation in different directions. The variance of noise across the images was visualised as images and with profiles across these images.ResultsThe most important finding was that the pattern of noise correlation is rotation symmetric or isotropic, independent of object shape in PET and PET/CT images reconstructed using the iterative method. This is, however, not the case in FBP images when the shape of phantom is not circular. Also CT images reconstructed using FBP show the same non-isotropic pattern independent of slice thickness and utilization of care dose function. SPECT images show an isotropic correlation of the noise independent of object shape or applied reconstruction algorithm. Noise in PET/CT images was identical independent of the applied X-ray dose in the transmission part (CT), indicating that the noise from transmission with the applied doses does not propagate into the PET images showing that the noise from the emission part is dominant. The results indicate that in human studies it is possible to utilize a low dose in transmission part while maintaining the noise behaviour and the quality of the images.ConclusionThe combined effect of noise correlation for asymmetric objects and a varying noise variance across the image field significantly complicates the interpretation of the images when statistical methods are used, such as with statistical estimates of precision in average values, use of statistical parametric mapping methods and principal component analysis. Hence it is recommended that iterative reconstruction methods are used for such applications. However, it is possible to calculate the noise analytically in images reconstructed by FBP, while it is not possible to do the same calculation in images reconstructed by iterative methods. Therefore for performing statistical methods of analysis which depend on knowing the noise, FBP would be preferred.

The objective of this study was to evaluate the radiation dose reduction potential of a novel image-based denoising technique in pediatric abdominopelvic and chest CT examinations and compare it with a commercial iterative reconstruction method. Data were retrospectively collected from 50 (25 abdominopelvic and 25 chest) clinically indicated pediatric CT examinations. For each examination, a validated noise-insertion tool was used to simulate half-dose data, which were reconstructed using filtered back-projection (FBP) and sinogram-affirmed iterative reconstruction (SAFIRE) methods. A newly developed denoising technique, adaptive nonlocal means (aNLM), was also applied. For each of the 50 patients, three pediatric radiologists evaluated four datasets: full dose plus FBP, half dose plus FBP, half dose plus SAFIRE, and half dose plus aNLM. For each examination, the order of preference for the four datasets was ranked. The organ-specific diagnosis and diagnostic confidence for five primary organs were recorded. The mean (± SD) volume CT dose index for the full-dose scan was 5.3 ± 2.1 mGy for abdominopelvic examinations and 2.4 ± 1.1 mGy for chest examinations. For abdominopelvic examinations, there was no statistically significant difference between the half dose plus aNLM dataset and the full dose plus FBP dataset (3.6 ± 1.0 vs 3.6 ± 0.9, respectively; p = 0.52), and aNLM performed better than SAFIRE. For chest examinations, there was no statistically significant difference between the half dose plus SAFIRE and the full dose plus FBP (4.1 ± 0.6 vs 4.2 ± 0.6, respectively; p = 0.67), and SAFIRE performed better than aNLM. For all organs, there was more than 85% agreement in organ-specific diagnosis among the three half-dose configurations and the full dose plus FBP configuration. Although a novel image-based denoising technique performed better than a commercial iterative reconstruction method in pediatric abdominopelvic CT examinations, it performed worse in pediatric chest CT examinations. A 50% dose reduction can be achieved while maintaining diagnostic quality.

This paper introduces a new accurate two-dimensional (2D) computer tomography reconstruction method, differentiated backprojection (DBP) and Hilbert filtering method. This method consists of two steps. First, form a backprojected image after taking the derivative of the parallel projection data. Second, apply Hilbert filtering along certain lines in the DBP image. Different from traditional filtered backprojection (FBP) algorithm, region of interest (ROI) can be reconstructed from truncated projection data in certain situation with this new method. A modified method is also presented. We carry out these three methods: DBP and Hilbert filtering method, its modified method, and FBP algorithm. Simulation results are presented that illustrate similar reconstructed image quality using this new method compared to FBP algorithm, and that show the capability to accurately reconstruct ROI from truncated projections.

Photoacoustic computed tomography (PACT) has emerged as a unique and promising technology for multiscale biomedical imaging. To fully realize its potential for various preclinical and clinical applications, development of systems with high imaging speed, reasonable cost, and manageable data flow are needed. Sparse-sampling PACT with advanced reconstruction algorithms, such as compressed-sensing reconstruction, has shown potential as a solution to this challenge. However, most such algorithms require iterative reconstruction and thus intense computation, which may lead to excessively long image reconstruction times. Here, we developed a principal component analysis (PCA)-based PACT (PCA-PACT) that can rapidly reconstruct high-quality, three-dimensional (3-D) PACT images with sparsely sampled data without requiring an iterative process. In vivo images of the vasculature of a human hand were obtained, thus validating the PCA-PACT method. The results showed that, compared with the back-projection (BP) method, PCA-PACT required ∼50% fewer measurements and ∼40% less time for image reconstruction, and the imaging quality was almost the same as that for BP with full sampling. In addition, compared with compressed sensing-based PACT, PCA-PACT had approximately sevenfold faster imaging speed with higher imaging accuracy. This work suggests a promising approach for low-cost, 3-D, rapid PACT for various biomedical applications.

Objective To study the effect of the reconstruction method on the semi-quantitative distribution of dopamine transporter (DAT) in the brain, 2β-carbomethoxy-3β-(4-fluorophe-nyl)-(N-11C-methyl)tropane (11C-CFT) PET images of healthy subjects were reconstructed by different PET reconstruction methods. Methods From March 2014 to June 2015, the 11C-CFT PET images of 41 healthy subjects were reconstructed by filtering back projection(FBP) method and ordered subsets expectation maximization (OSEM) iterative method. The brain regions of interest (ROI), namely, caudate nucleus, anterior putamen, and posterior shell nucleus, were automatically sketched with the parietal and occipital cortex lacking of DAT distribution as reference regions. The semi-quantitative value of DAT distribution was calculated using the following formula: radioactivity count of ROI/radioactivity count of parietal and occipital cortex-1. Paired t-test was used to compare the semi-quantitative values of DAT distribution. Correlation analysis was performed using the Pearson correlation analysis. Results The values of DAT distribution based on OSEM were as follows: caudate nucleus (1.77-2.15), anterior putamen (2.17-2.39), and posterior putamen (1.71-2.06). The values of DAT distribution based on FBP were as follows: caudate nucleus (1.68-2.10), anterior putamen (2.07-2.37), and posterior putamen (1.62-1.96). In the bilateral caudate nucleus and anterior and posterior putamen, the 11C-CFT of DAT distribution by OSEM was significantly higher than that by FBP(t=9.658-15.859, all P=0.000). The Pearson correlation analysis showed that the semi-quantitative values of DAT distribution by FBP and OSEM were positively correlated with each other in the bilateral caudate nucleus and anterior and posterior putamen (R2=0.907-0.951, all P=0.000). The DAT distribution by OSEM and FBP decreased with aging in the caudate nucleus and anterior and posterior putamen. Conclusions A significant difference was found in the semi-quantitative value of the DAT distribution in the brain of healthy subjects by different PET reconstruction methods. Therefore, a consistent PET image reconstruction method should be used in a multicenter or longitudinal study. Key words: Dopamine plasma membrane transport proteins; Positron-emission tomography; Filtered backprojection; Iterative

Purpose: During diagnostic x‐ray CT imaging procedures or image guided radiotherapy, image quality will be degraded if target organs move during the data acquisition. This can be caused by patients' occasional motion or by intrinsic motion like cardiac and respiratory motion. The inconsistency in the projection data is the major reason for the image quality degradation. We present and validate a method to improve the consistency of the projections using a novel Fan‐beam Data Consistency Condition (FDCC) such that the image quality can be improved. Method and Materials: Computer‐simulated dynamic phantoms are generated and projection data are acquired from these dynamic phantoms. Using the FDCC, individual projection data from one view of fan‐beam projections can be estimated from filtering all the other projection data acquired from different view angles. Then those projections contaminated by motion are re‐estimated using the FDCC, resulting in a corrected sinogram. A standard Fan‐beam Filtered Back Projection (FBP) reconstruction algorithm is then used to reconstruct images from the corrected sinograms. Motion artifacts can be alleviated using this procedure. Results: Images are reconstructed from both the original sinogram where projections are contaminated by motion and the corrected sinogram after applying the FDCC. Strong motion artifacts are observed in the images reconstructed from the contaminated sinogram while improvement can be found in the reconstructed images using the corrected sinogram. Conclusions: A novel method using the new FDCC is proposed to combat the motion artifacts due to the temporal inconsistency in the projection data. Numerical simulations were conducted to demonstrate the potential of this correction scheme to mitigate motion artifacts. Thus, the preliminary numerical results indicate that the FDCC has potential use in combating both cardiac and respiratory motion in CT imaging.

In comparison with conventional filtered backprojection (FBP) algorithms for x-ray computed tomography (CT) image reconstruction, statistical algorithms directly incorporate the random nature of the data and do not assume CT data are linear, noiseless functions of the attenuation line integral. Thus, it has been hypothesized that statistical image reconstruction may support a more favorable tradeoff than FBP between image noise and spatial resolution in dose-limited applications. The purpose of this study is to evaluate the noise-resolution tradeoff for the alternating minimization (AM) algorithm regularized using a nonquadratic penalty function. Idealized monoenergetic CT projection data with Poisson noise were simulated for two phantoms with inserts of varying contrast (7%-238%) and distance from the field-of-view (FOV) center (2-6.5 cm). Images were reconstructed for the simulated projection data by the FBP algorithm and two penalty function parameter values of the penalized AM algorithm. Each algorithm was run with a range of smoothing strengths to allow quantification of the noise-resolution tradeoff curve. Image noise is quantified as the standard deviation in the water background around each contrast insert. Modulation transfer functions (MTFs) were calculated from six-parameter model fits to oversampled edge-spread functions defined by the circular contrast-insert edges as a metric of local resolution. The integral of the MTF up to 0.5 1p/mm was adopted as a single-parameter measure of local spatial resolution. The penalized AM algorithm noise-resolution tradeoff curve was always more favorable than that of the FBP algorithm. While resolution and noise are found to vary as a function of distance from the FOV center differently for the two algorithms, the ratio of noises when matching the resolution metric is relatively uniform over the image. The ratio of AM-to-FBP image variances, a predictor of dose-reduction potential, was strongly dependent on the shape of the AM's nonquadratic penalty function and was also strongly influenced by the contrast of the insert for which resolution is quantified. Dose-reduction potential, reported here as the fraction (%) of FBP dose necessary for AM to reconstruct an image with comparable noise and resolution, for one penalty parameter value of the AM algorithm was found to vary from 70% to 50% for low-contrast and high-contrast structures, respectively, and from 70% to 10% for the second AM penalty parameter value. However, the second penalty, AM-700, was found to suffer from poor low-contrast resolution when matching the high-contrast resolution metric with FBP. The results of this simulation study imply that penalized AM has the potential to reconstruct images with similar noise and resolution using a fraction (10%-70%) of the FBP dose. However, this dose-reduction potential depends strongly on the AM penalty parameter and the contrast magnitude of the structures of interest. In addition, the authors' results imply that the advantage of AM can be maximized by optimizing the nonquadratic penalty function to the specific imaging task of interest. Future work will extend the methods used here to quantify noise and resolution in images reconstructed from real CT data.

Volumetric measurement of artificial pure ground-glass nodules at low-dose CT: Comparisons between hybrid iterative reconstruction and filtered back projection

Previously the Orthogonal Polynomial Expansion on the Disk (OPED) algorithm was presented. Further, in prototype experiments in combination with the CT D`or geometry feasibility was demonstrated. In this study we implemented OPED with a clinical Scanner, and evaluated the potential using phantom studies. All studies were acquired on a Siemens Somatom 64 (Erlangen, Germany) scanner, where raw projection data were reconstructed with the conventional FBP reconstruction and the OPED algorithm. OPED allows one to use fan beam geometry directly without any additional procedures such as interpolation or rebinning if using the CT D`or geometry. In particular, OPED describes an approximation of the image function as a sum of polynomials using Chebychev polynomials. For performance evaluation, the Catphan phantom 600 was imaged. OPED Images where reconstructed using C++ and MATLAB® .We measured uniformity, MTF and CNR for different dose levels and compared these to standard FBP images reconstructions with different filter kernels. The integration and interpretation of the MDCT projection data for the OPED algorithm was accomplished. Reconstruction time is about 6 s on Quad-Core 3 GHz Intel Xeon processor. Typical artifacts are reduced when applying OPED. Using OPED the MTF maintains constant over the whole FOV. Uniformity and CNR are equal compared to FBP. Advantages of OPED were demonstrated by applying the algorithm to projections images from a clinical MDCT scanner. In the future, we see OPED applications for low-dose or limited angle geometries to reduce the radiation dose while improving diagnostic quality of the reconstructed slices.

To evaluate the image quality and radiation dose reduction in pelvic computed tomography (CT) achieved with an adaptive iterative dose reduction 3-dimensional (AIDR 3D) algorithm using a phantom model. Two phantoms were scanned using a 320-detector row CT scanner with 8 tube current levels, and the images were reconstructed with a standard filtered back projection (FBP) algorithm and with an AIDR 3D algorithm. Compared with FBP, AIDR 3D reduced image noise and improved contrast-to-noise ratios. The diagnostic performance for detection of low-contrast targets of AIDR 3D images obtained with 100 mA at 120 kVp was almost as good as that of the FBP images obtained with 200 mA. The AIDR 3D algorithm substantially reduced image noise and improved the image quality of pelvic CT images compared with those obtained with the FBP algorithm and can thus be considered a promising technique for low-dose pelvic CT examinations.

Computed Tomography (CT) using Carbon Nanotube (CNT) x-ray source is a technique of generating reconstruction images of the structure of teeth sample. A proto type CNT x-ray CT was designed for medical imaging to examine whether it could be used to analysis the equipment of medical and industrial application. The CNT field emitter array was grown on silicon substrate through a resist-assisted patterning (RAP) process. The field emission properties showed a gate turn-on field of 3.8 V/μm at an anode emission current of 0.5 mA. The author demonstrated the x-ray source with four electrode structures utilizing the CNT emitter. The acquisitioned images were reconstructed by filtered back projection (FBP) method.

In computed tomography (CT), metal objects in the scanning filed are accompanied by physical phenomenon that causes projections to be inconsistent. These inconsistencies produce bright and dark shadows or streaks in analytically reconstructed images. Interpolation-based metal artifact reduction (MAR) algorithms usually replace the inconsistent projection data by estimating surrogate data based on the surrounding uncorrupted projections. In such cases, secondary artifacts will be generated when the data estimates are inaccurate. Therefore, better projection estimation is critical. This paper proposes an image post-processing strategy to create an intermediate image, named the prior image and better estimates of the surrogate data by forward projecting this prior image. The proposed method consists of three steps based on the forward projection MAR framework. First, metallic implants in the uncorrected images are segmented using a Markov random field model (MRF). Then a prior image is generated via an edge-preserving filter and a recovery procedure of the adjacent anatomical structures. Finally, the projection is completed via forward projecting this prior image and the corrected image is reconstructed by the filtered backprojection (FBP) method. Studies on both phantom and clinical data are carried out to verify the performance of the proposed method. The comparisons with other previous MAR algorithms demonstrate that the proposed MAR method performs better in metal artifact suppression and anatomical structure preservation.

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose X-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (1) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (2) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N<formula>^3</formula>), where N is the number of pixel in one dimension.

Dose and image quality are two important parameters in CT Scan examination. The radiation dose produced at the CT scan is far greater than the radiation dose of the conventional radiological examination, so the utilization must be as good as possible. On Siemens CT Scan there is an automatic exposure control software, with expectations that the radiation dose received by the patient can be reduced because the software is an auto mA that is adjusted to the thickness of the object, but the impact of using the software causes a decrease in image quality, so it needs to be done image improvement using a back projection filter (BPF). Experimental research by applying a back projection filter to the Scan Head image on axial sections. Image assessment using 2 radiologists with data analysis using statistical processing and image post processing. CT Scan image information Head axial pieces experience differences in image information between before and after the back projection, with the mean value in each group experiencing an increase in image quality in the group after a back projection filter. Where the image after the back projection filter by applying automatic exposure control with kV 110 is the most optimal kV.