An iteration algorithm in dual-energy x-ray imaging based on polychromatic physics model

Dual-energy X-ray imaging is an important method of medical imaging, capable of not only obtaining spatial information of imaging object but also disclosing its chemical components, and has many applications in clinic. The current computation methods of dual-energy imaging are still based on the model of mono-energy spectrum imaging with some linear calibration, while they are incapable to reflect correctly the physical characteristics of dual-energy imaging and obstruct deeper research in this field. The article presents a new medical X-ray imaging model in accordance with physics of imaging and its corresponding computational method. The computation process includes two steps: first, to compute two attenuation parameters that have clear physical meaning: equivalent electron density and attenuation parameter of photoemission; then to compute the components of high- and low-density mass through a group of simple equation with two variables. Experiments showed that such method has quite a satisfactory precision in theory, that is, the solutions of parameters under different exposure voltages and thickness of tissue for several main tissues of human body are much low in deviations, whose quotient of standard deviation divided by mean are mostly under 0.1%, and at most 0.32%. The method provides not only a new computational way for dual-energy X-ray imaging, but also a feasible analysis for its nature. In addition, the method can be used to linearly rectify data of dual-energy CT and analyze the chemical component of reconstructed object by means of parameters clear in physics.

Medical Imaging has been playing one of the most important roles in medical diagnosis. As the technologies advance, so does medical imaging, and it gets an increasing role, not only in diagnosis, but also in treatment, such as image-guided therapies. Medical imaging also has a great impact on many research areas including neuroscience, drug development, phycology, psychiatry, cardiology, and so on. Advancement of the medical imaging technologies involves multidisciplinary research fields that encompass physics, medicine, electrical and mechanical engineering, biology and chemical engineering, etc. Considering the impact of medical imaging on clinics, research, and engineering, we select “Medical Imaging” as the theme of this Special Issue of Biomedical Engineering Letters. This special issue includes five review papers on recent advances of several medical imaging technologies and their applications. The first review paper entitled, “Model based filtered backprojection algorithm: a tutorial”, by Gengsheng L. Zeng, IEEE Fellow, USA, provides in-depth knowledge of very interesting new type of linear reconstruction algorithm with incorporation of noise models in it [1]. For many decades, the filtered backprojection (FBP) algorithm has been a popular choice in image reconstruction. However, recent developments of new medical imaging systems such as lowdose x-ray CT, nuclear medicine, and real-time MRI applications require more advanced reconstruction algorithms than the conventional FBP in order to incorporate measurement noise and system models. In recent years, many researchers have been developing various iterative algorithms to meet this demand and improve the final reconstructed images. However, the drawback of most iterative algorithms is the heavy computational cost. Therefore, it would be wonderful if we could have an FBP algorithm that performs comparable tasks to the iterative algorithms. In this first review paper, Dr. Zeng provides a way to develop such an FBP algorithm with incorporation of noise models, which may replace the state-of-the-art iterative algorithms. The second review paper, “Challenges and advances in MR imaging of the intervertebral disc could the cartilaginous endplate be a biomarker for the disc health?,” by Sung M. Moon, Ph.D., GE Healthcare, USA, provides an overview of new magnetic resonance imaging (MRI) techniques and findings on disc disease and cartilaginous endplate (CEP) [2]. A brief description on the anatomy of the CEP and intervertebral disc is followed by their roles in the disc Dosik Hwang ( ) School of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea Tel : +82-2-2123-5771 E-mail : dosik.hwang@yonsei.ac.kr

The purpose of this article is to study the added value of model-based iterative reconstruction (MBIR) on metal artifact reduction on CT compared with standard filtered back projection (FBP). Ex vivo imaging was performed on several metal implants. Datasets were reconstructed with standard FBP and MBIR algorithms. The sizes of the artifacts surrounding the metal implant were recorded and compared. In vivo imaging was performed on 62 patients with metal implants. Each dataset was reconstructed with FBP and MBIR algorithms. Objective image quality was assessed by measuring the size of the artifact generated by the metal implant. Subjective image quality was graded on a 3-point scale, taking into account the visibility of the bone-metal interface, as well as the visibility of the neighboring soft tissues. Ex vivo analysis yielded a reduction of 82% in the size of the artifact when using the MBIR algorithm, compared with the FBP algorithm. The mean (SD) size of the artifacts was 1.4 ± 0.8 and 0.25 ± 0.06 cm(2) with FBP and MBIR, respectively. In vivo, the mean size of the artifacts decreased from 7.3 ± 1.5 cm(2) to 4.0 ± 0.9 cm(2) for FBP and MBIR, respectively (p = 0.012). The subjective image quality analysis showed an equal or better bone-metal interface of MBIR algorithm in 85% of cases. Visibility of the soft tissue surrounding the metal implant was determined to be equal or better in 97% of cases in which MBIR was used. This study shows that the MBIR algorithm allows a clear reduction of metal artifacts on CT images and, hence, a better analysis of the soft tissue surrounding the metal implant compared with FBP.

Filtered back-projection (FBP) is the most commonly used reconstruction method for PET images, which are usually noisy. The iterative reconstruction segmented attenuation correction (IRSAC) algorithm improves image quality without reducing image resolution. The standardized uptake value (SUV) is the most clinically utilized quantitative parameter of [fluorine-18]fluoro-2-deoxy-D-glucose (FDG) accumulation. The objective of this study was to obtain a table of SUVs for several normal anatomical structures from both routinely used FBP and IRSAC reconstructed images and to compare the data obtained with both methods. Twenty whole-body PET scans performed in consecutive patients with proven or suspected non-small cell lung cancer were retrospectively analyzed. Images were processed using both IRSAC and FBP algorithms. Nonquantitative or gaussian filters were used to smooth the transmission scan when using FBP or IRSAC algorithms, respectively. A phantom study was performed to evaluate the effect of different filters on SUV. Maximum and average SUVs (SUVmax and SUVavg) were calculated in 28 normal anatomical structures and in one pathological site. The phantom study showed that the use of a nonquantitative smoothing filter in the transmission scan results in a less accurate quantification and in a 20% underestimation of the actual measurement. Most anatomical structures were identified in all patients using the IRSAC images. On average, SUVavg and SUVmax measured on IRSAC images using a gaussian filter in the transmission scan were respectively 20% and 8% higher than the SUVs calculated from conventional FBP images. Scatterplots of the data values showed an overall strong relationship between IRSAC and FBP SUVs. Individual scatterplots of each site demonstrated a weaker relationship for lower SUVs and for SUVmax than for higher SUVs and SUVavg. A set of reference values was obtained for SUVmax and SUVavg of normal anatomical structures, calculated with both IRSAC and FBP image reconstruction algorithms. The use of IRSAC and a gaussian filter for the transmission scan seems to give more accurate SUVs than are obtained from conventional FBP images using a nonquantitative filter for the transmission scan.

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.

To explore the application value of the reconstruction algorithm based on an iterative algorithm in the analysis of CT image and analyze the therapeutic effect of honey-fried Herba Ephedrae combined with Western medicine on acute exacerbation chronic obstructive pulmonary disease (AECOPD), a total of 96 AECOPD patients admitted to our hospital from January 2018 to December 2019 were selected as research subjects. According to a different treatment method, the subjects were divided into a control group (Ctrl group, conventional therapy) and an observation group (OG, conventional therapy + honey-fried Herba Ephedrae), with 48 in each group. The CT image algorithm was established based on the iterative algorithm, and the CT dose indexes of the reconstruction algorithm and the Filtered Back Projection (FBP) algorithm under the same conditions were compared ( P < 0.05 ). After using CT to confirm the diagnosis of the subjects, the difference in indicators of forced expiratory volume in one second (FEV1), forced expiratory volume in one second to forced vital capacity ratio (FEV1%), and forced vital capacity (FVC), inflammatory factors of serum interleukin-8 (IL-8), serum interleukin-10 (IL-10), and tumor necrosis factor (TNF-α), the bronchial wall area, and the total treatment efficiency before and after different treatment was analyzed. The results suggested that the Computed Tomography Dose Index (CTDI) of iterative reconstruction (IR) algorithm when scanning different parts was higher than that of the FBP algorithm. The pulmonary function indexes and the expression of IL-8 and TNF-α in the OG were higher than those in the Ctrl group ( P < 0.05 ); the bronchial wall area, bronchial wall area percentage, and IL-10 expression in the OG were all lower than those in the Ctrl group ( P < 0.05 ). The effectiveness and improvement rates of the Ctrl group were 47.92% and 25%, respectively, significantly lower than those in the OG group, 56.25% and 31.25% ( P < 0.05 ), and the total efficiency of the observation group was 87.5%, which was significantly higher than that in the Ctrl group (72.92%) ( P < 0.05 ). In conclusion, based on the iterative algorithm, a CT reconstruction algorithm with better noise reduction performance was established, and the use of honey-fried Herba Ephedrae combined with Western medicine can improve the effective rate of treatment.

Prospective Evaluation of Dual-Energy Imaging in Patients Undergoing Image Guided Radiation Therapy for Lung Cancer: Initial Clinical Results

Iterative algorithms are gaining clinical acceptance in CT. We performed objective phantom-based image quality evaluation of five commercial iterative reconstruction algorithms available on four different multi-detector CT (MDCT) scanners at different dose levels as well as the conventional filtered back-projection (FBP) reconstruction. Using the Catphan500 phantom, we evaluated image noise, contrast-to-noise ratio (CNR), modulation transfer function (MTF) and noise-power spectrum (NPS). The algorithms were evaluated over a CTDIvol range of 0.75-18.7 mGy on four major MDCT scanners: GE DiscoveryCT750HD (algorithms: ASIR™ and VEO™); Siemens Somatom Definition AS+ (algorithm: SAFIRE™); Toshiba Aquilion64 (algorithm: AIDR3D™); and Philips Ingenuity iCT256 (algorithm: iDose4™). Images were reconstructed using FBP and the respective iterative algorithms on the four scanners. Use of iterative algorithms decreased image noise and increased CNR, relative to FBP. In the dose range of 1.3-1.5 mGy, noise reduction using iterative algorithms was in the range of 11%-51% on GE DiscoveryCT750HD, 10%-52% on Siemens Somatom Definition AS+, 49%-62% on Toshiba Aquilion64, and 13%-44% on Philips Ingenuity iCT256. The corresponding CNR increase was in the range 11%-105% on GE, 11%-106% on Siemens, 85%-145% on Toshiba and 13%-77% on Philips respectively. Most algorithms did not affect the MTF, except for VEO™ which produced an increase in the limiting resolution of up to 30%. A shift in the peak of the NPS curve towards lower frequencies and a decrease in NPS amplitude were obtained with all iterative algorithms. VEO™ required long reconstruction times, while all other algorithms produced reconstructions in real time. Compared to FBP, iterative algorithms reduced image noise and increased CNR. The iterative algorithms available on different scanners achieved different levels of noise reduction and CNR increase while spatial resolution improvements were obtained only with VEO™. This study is useful in that it provides performance assessment of the iterative algorithms available from several mainstream CT manufacturers.

Filtered backprojection (FBP) algorithms are commonly employed for image reconstruction in optoacoustic tomography (OAT). A limitation of FBP algorithms is that they require the measured acoustic data to be densely sampled, which necessitates expensive ultrasound arrays that possess a large number of elements or increased data-acquisition times if mechnical scanning is employed. Additionally, FBP algorithms are based on idealized imaging models that do not accurately model the response of the transducers and fail to exploit the statistical characteristics of noisy measurement data to minimize noise levels in the reconstructed images. Iterative image reconstruction algorithms can circumvent these difficulties. However, to date, iterative reconstruction algorithms have not been successfully applied to three-dimensional (3D) OAT. In this work we investigate the use of an iterative image reconstruction method in 3D OAT. The large computational burden of 3D iterative image reconstruction is circumvented by implementing the reconstrution algorithm with graphics processing units (GPUs). The ability of the reconstruction algorithm to mitigate artifacts due to incomplete data is demonstrated.

This paper presents a comparison between an analytical and a statistical iterative reconstruction algorithm for computed transmission tomography concerning their noise and resolution performance. The reconstruction of two-dimensional images from simulated fan-beam transmission data is performed with a filtered back-projection (FBP) type reconstruction and an iterative ordered subsets convex (OSC) maximum-likelihood method. A special software phantom, which allows measuring the resolution and noise in a nonambiguous way, is used to simulate transmission tomography scans with different signal-to-noise ratios (SNR). The noise and modulation transfer function is calculated for FBP and OSC reconstruction at several positions, distributed over the field-of-view (FOV). The reconstruction with OSC using different numbers of subsets shows an inverse linear relation to the number of iterations that are necessary to reach a certain resolution and SNR, i.e., increasing the number of subsets by a factor x reduces the number of required iterations by the same factor. The OSC algorithm is able to achieve a nearly homogeneous high resolution over the whole FOV, which is not achieved with FBP. The OSC method achieves a lower level of noise compared with FBP at the same resolution. The reconstruction with OSC can save a factor of up to nine of x-ray dose compared with FBP in the investigated range of noise levels.

In this paper, the reconstruction of axisymmetric temperature and H2O concentration distributions in a flat flame burner is realized by tunable diode laser absorption spectroscopy (TDLAS) and filtered back-projection (FBP) algorithm. Two H2O absorption transitions (7154.354/7154.353 cm-1 and 7467.769 cm-1) are selected as line pair for temperature measurement, and time division multiplexing technology is adopted to scan this two H2O absorption transitions simultaneously at 1 kHz repetition rate. In the experiment, FBP algorithm can be used for reconstructing axisymmetric distributions of flow field parameters with only single view parallel-beam TDLAS measurements, and the same data sets from the given parallel beam are used for other virtual projection angles and beams scattered between 0° and 180°. The real-time online measurements of projection data, i.e., integrated absorbance both for pre-selected transitions on CH4/air flat flame burner are realized by Voigt on-line fitting, and the fitting residuals are less than 0.2%. By analyzing the projection data from different views based on FBP algorithm, the distributions of temperature and concentration along radial direction can be known instantly. The results demonstrate that the system and the proposed innovative FBP algorithm are capable for accurate reconstruction of axisymmetric temperature and H2O concentration distribution in combustion systems and facilities.

In single photon emission computed tomography (SPECT), a varying-focal-length cone-beam collimator can be used to reduce the truncation problem and to maintain sensitivity when imaging the organ of interest. The collimator is constructed so that the collimator holes focus to a circular symmetric, spatially varying, focal point function. The focal length increases radially from the shortest focal length at the centre to the longest focal length at the periphery of the collimator. This paper describes a 3D backprojection-filtering (BF) algorithm for this varying-focal-length cone-beam geometry. The proposed algorithm is compared to an iterative ML-EM (maximum likelihood-expectation maximization) algorithm. The 3D Hoffman brain phantom and Defrise phantom are used in computer simulations. Since the maximum tilt angle of the projection rays is small for most realistic imaging geometries, the proposed algorithm provides a good approximation. When a circular orbit is used, the BF algorithm gives an exact reconstruction of the central slice.

Most material discrimination in security inspections is based on dual-energy x-ray imaging, which enables the determination of a material’s effective atomic number (Zeff) as well as electron density and its consequent classification as organic or inorganic. Recently phase-based ‘dark-field’ x-ray imaging approaches have emerged that are sensitive to complementary features of a material, namely its unresolved microstructure. It can therefore be speculated that their inclusion in the security-based imaging could enhance material discrimination, for example of materials with similar electron densities and Zeff but different microstructures. In this paper, we present a preliminary evaluation of the advantages that such a combination could bear. Utilising an energy-resolved detector for a phase-based dark-field technique provides dual-energy attenuation and dark-field images simultaneously. In addition, since we use a method based on attenuating x-ray masks to generate the dark-field images, a fifth (attenuation) image at a much higher photon energy is obtained by exploiting the x-rays transmitted through the highly absorbing mask septa. In a first test, a threat material is imaged against a non-threat one, and we show how their discrimination based on maximising their relative contrast through linear combinations of two and five imaging channels leads to an improvement in the latter case. We then present a second example to show how the method can be extended to discrimination against more than one non-threat material, obtaining similar results. Albeit admittedly preliminary, these results indicate that significant margins of improvement in material discrimination are available by including additional x-ray contrasts in the scanning process.

Proton CT (pCT) has the potential to accurately measure the electron density map of tissues at low doses but the spatial resolution is prohibitive if the curved paths of protons in matter is not accounted for. The authors propose to account for an estimate of the most likely path of protons in a filtered backprojection (FBP) reconstruction algorithm. The energy loss of protons is first binned in several proton radiographs at different distances to the proton source to exploit the depth-dependency of the estimate of the most likely path. This process is named the distance-driven binning. A voxel-specific backprojection is then used to select the adequate radiograph in the distance-driven binning in order to propagate in the pCT image the best achievable spatial resolution in proton radiographs. The improvement in spatial resolution is demonstrated using Monte Carlo simulations of resolution phantoms. The spatial resolution in the distance-driven binning depended on the distance of the objects from the source and was optimal in the binned radiograph corresponding to that distance. The spatial resolution in the reconstructed pCT images decreased with the depth in the scanned object but it was always better than previous FBP algorithms assuming straight line paths. In a water cylinder with 20 cm diameter, the observed range of spatial resolutions was 0.7 - 1.6 mm compared to 1.0 - 2.4 mm at best with a straight line path assumption. The improvement was strongly enhanced in shorter 200° scans. Improved spatial resolution was obtained in pCT images with filtered backprojection reconstruction using most likely path estimates of protons. The improvement in spatial resolution combined with the practicality of FBP algorithms compared to iterative reconstruction algorithms makes this new algorithm a candidate of choice for clinical pCT.

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm.