An experimental study on DBP and Hilbert filtering method for tomography reconstruction

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.

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 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.

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.

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

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.

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.

Investigates the performance of exact reconstruction algorithms for spiral cone-beam computed tomography. The authors compare two different approaches of exact algorithms: the first one is the Radon algorithm with explicit calculation of Radon data and subsequent direct inversion, the second approach is a reformulation of the Radon algorithm as a three-dimensional (3-D) filtered backprojection (FBP) method. Both algorithms are able to reconstruct a region of interest (ROI) of a long object by using the local ROI technique. The goal of this study is to identify which algorithm has the better performance with respect to image quality and practicability. The properties of the algorithms are analyzed. Image quality is evaluated regarding artifacts, spatial as well as contrast resolution, and noise properties. The 3-D point spread function (PSF) is examined for violations of isotropy and spatial invariance. In-plane and axial resolutions are derived from the in-plane modulation transfer function (MTF) and the slice sensitivity profile (SSP), respectively. The results show that for the two implementations investigated in this study, the image quality is similar, with a slight advantage of the FBP case. The algorithms yield images almost free of artifacts but with a poor spatial resolution. Regarding practicability, however, the FBP approach seems to be a more convenient and more flexible method because of the sequential processing of the projections and the easy control of image characteristics.

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.

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

This paper presents a new type of filtered backprojection (FBP) algorithm for fan-beam full- and partial-scans. The filtering is shift-invariant with respect to the angular variable. The backprojection does not include position-dependent weights through the Hilbert transform and the one-dimensional transformation between the fan- and parallel-beam coordinates. The strong symmetry of the filtered projections directly leads to an exact reconstruction for partial data. The use of the Hilbert transform avoids the approximation introduced by the nonuniform cutoff frequency required in the ramp filter-based FBP algorithm. Variance analysis indicates that the algorithm might lead to a better uniformity of resolution and noise in the reconstructed image. Numerical simulations are provided to evaluate the algorithm with noise-free and noisy projections. Our simulation results indicate that the algorithm does have better stability over the ramp-filter-based FBP and circular harmonic reconstruction algorithms. This may help improve the image quality for in place computed tomography scanners with single-row detectors.

X-ray Computed Tomography (CT) is widely used in clinical diagnosis. However, the requirement of numerous projections collected in a full-angular range hinders CT image-guided applications such as real-time biopsy. This paper mainly discusses the most challenging single view CT reconstruction problem to speed up the CT-guided clinical workflow. We propose a deep learning approach for single-view CT reconstruction guided by Filtered Back Projection (FBP) algorithm which makes the single view reconstruction accurate, fast and interpretable. We formulate an end-to-end framework that contains the projection generation network to predict sufficient projections from a single view, the FBP layer to obtain coarse CT volume, and the CT fine-tuning network to output the final CT volume. We carefully design our training strategy to ensure the network towards CT reconstruction. Our experiments on the public 4D CT datasets prove that our method achieves state-of-the-art performance.

Targeted-ROI imaging in electron paramagnetic resonance imaging

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.

In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence property of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE-EM, and have performance advantages over FBP in terms of contrast recovery and/or noise-to-signal ratios (NSRs) in regions of interest.