Hilbert Transform Based FBP Algorithm for Fan-Beam CT Full and Partial Scans

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.

PET images reconstructed using the filtered backprojection (FBP) algorithm have the advantage of being unbiased but at the cost of exhibiting a high variance. The latter effect is often the dominant factor in clinical practice. Recently we have proposed new families of filters for FBP reconstruction that were designed so that the FBP reconstructions using these filters emulate the error properties of OSEM reconstructions (i.e. exhibiting some level of bias but with reduced variance). In this study these families of filters are used as the reconstruction filters prior to backprojection in iterative FBP (IFBP). Using these filters the convergence rate of the IFBP algorithm can be controlled. Two well known special cases correspond to the conventional IFBP with ramp filter and the Landweber method, reaching the highest and lowest convergence speeds respectively. In addition the range of filters in the filter family allows exploration of a range of bias variance trade-off curves, with the Landweber method reaching the lowest mean squared error (MSE). Additionally optional non-negativity constraints can be included allowing still different bias variance trade-offs. In conclusion it is found that the use of filters with a lower inversion power result in a slower convergence of the IFBP algorithm but the resulting images can reach a lower MSE. It is shown that, for a cold region, adding the non-negativity constraint effectively reduces the variance but at the cost of introducing a bias. For a range of filters from the new filter families, it is found that the IFBP algorithm using these filters can outperform both the conventional IFBP using the ramp filter, FBP and OSEM reconstructions in terms of MSE. The optional non-negativity constraint can aid in further reducing the MSE depending on the ROI and ROI size. Therefore, using the new filters in FBP permits a compromise between reconstruction speed and the reconstruction error.

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, 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.

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.

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.

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.

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

To prospectively compare traditional filtered back projection (FBP) and iterative image reconstruction for the evaluation of heavily calcified arteries with coronary computed tomography (CT) angiography. The study had institutional review board approval and was HIPAA compliant. Written informed consent was obtained from all patients. Fifty-five consecutive patients (35 men, 20 women; mean age, 58 years ± 12 [standard deviation]) with Agatston scores of at least 400 underwent coronary CT angiography and cardiac catheterization. Image data were reconstructed with both FBP and iterative reconstruction techniques with corresponding cardiac algorithms. Image noise and subjective image quality were compared. To objectively assess the effect of FBP and iterative reconstruction on blooming artifacts, volumes of circumscribed calcifications were measured with dedicated volume analysis software. FBP and iterative reconstruction series were independently evaluated for coronary artery stenosis greater than 50%, and their diagnostic accuracy was compared, with cardiac catheterization as the reference standard. Statistical analyses included paired t tests, Kruskal-Wallis analysis of variance, and a modified McNemar test. Image noise measured significantly lower (P = .011-.035) with iterative reconstruction instead of FBP. Image quality was rated significantly higher (P = .031 and .042) with iterative reconstruction series than with FBP. Calcification volumes measured significantly lower (P = .019 and .026) with iterative reconstruction (44.3 mm(3) ± 64.7 and 46.2 mm(3) ± 68.8) than with FBP (54.5 mm(3) ± 69.5 and 56.3 mm(3) ± 72.5). Iterative reconstruction significantly improved some measures of per-segment diagnostic accuracy of coronary CT angiography for the detection of significant stenosis compared with FBP (accuracy: 95.9% vs 91.8%, P = .0001; specificity: 95.8% vs 91.2%, P = .0001; positive predictive value: 76.9% vs 61.1%, P = .0001). Iterative reconstruction reduces image noise and blooming artifacts from calcifications, leading to improved diagnostic accuracy of coronary CT angiography in patients with heavily calcified coronary arteries.

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.

In this study, the filtered back-projection algorithm was used to reconstruct the photoacoustic imaging. To improve the quality of the reconstructed image, the wavelet threshold denoising method was combined into the filtered back-projection reconstruction algorithm. To obtain the reconstructed effect of the photoacoustic imaging, a modified wavelet threshold function was proposed. To verify the feasibility of the modified wavelet threshold function, the simulation experiments of the standard test phantom were performed by using three different wavelet threshold functions. Compared with the soft- and hard-threshold functions, the modified wavelet threshold function has better denoised and reconstructed effect. Moreover, the peak signal-to-noises ratio (PSNR) value of the modified function is largest, and its mean root square error (MRSE) value is lest than that of two others. Therefore, the filtered back-projection reconstruction algorithm combined with the modified wavelet threshold function has potential value in the reconstruction of the photoacoustic imaging.

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.

Effects of reconstruction technique on the quality of abdominal CT angiography: A comparison between forward projected model-based iterative reconstruction solution (FIRST) and conventional reconstruction methods

An adaptive, nonlinear image domain filtering strategy is described which improves positron emission tomography (PET) images. The method was formulated to improve on the linear, low-pass filtering typically applied to each projection in the filtered back-projection (FBP) reconstruction algorithm. The algorithm is a potential alternative to linear smoothing which reduces noise but degrades resolution; this method uses the FBP algorithm for reconstruction, but aims to incorporate some of the statistical information and nonlinear smoothing utilized in iterative reconstruction algorithms. The approach uses sinogram segmentation to separate the sinogram elements with higher and lower signal-to-noise ratios, and then reconstruct each with FBP using a more appropriate choice of filter and cut-off frequency. Also, this algorithm addresses the radial streak artifacts introduced by FBP. The algorithm was evaluated using simulations as well as clinical data of cardiac PET studies on an ECAT 931 PET scanner. The initial results suggest that this technique has advantages over the current clinical protocol. Images processed with the method show generally improved visual image quality and reduced radial streaks without the introduction of artifacts. Also, by using a higher resolution filter for the high activity segment of the sinogram, increased contrast recovery and resolution are realized.

Dynamic CT myocardial perfusion imaging has the potential to provide both functional and anatomical information regarding coronary artery stenosis. However, radiation dose can be potentially high due to repeated scanning of the same region. The purpose of this study is to investigate the use of statistical iterative reconstruction to improve parametric maps of myocardial perfusion derived from a low tube current dynamic CT acquisition. Four pigs underwent high (500 mA) and low (25 mA) dose dynamic CT myocardial perfusion scans with and without coronary occlusion. To delineate the affected myocardial territory, an N-13 ammonia PET perfusion scan was performed for each animal in each occlusion state. Filtered backprojection (FBP) reconstruction was first applied to all CT data sets. Then, a statistical iterative reconstruction (SIR) method was applied to data sets acquired at low dose. Image voxel noise was matched between the low dose SIR and high dose FBP reconstructions. CT perfusion maps were compared among the low dose FBP, low dose SIR and high dose FBP reconstructions. Numerical simulations of a dynamic CT scan at high and low dose (20:1 ratio) were performed to quantitatively evaluate SIR and FBP performance in terms of flow map accuracy, precision, dose efficiency, and spatial resolution. Forin vivo studies, the 500 mA FBP maps gave -88.4%, -96.0%, -76.7%, and -65.8% flow change in the occluded anterior region compared to the open-coronary scans (four animals). The percent changes in the 25 mA SIR maps were in good agreement, measuring -94.7%, -81.6%, -84.0%, and -72.2%. The 25 mA FBP maps gave unreliable flow measurements due to streaks caused by photon starvation (percent changes of +137.4%, +71.0%, -11.8%, and -3.5%). Agreement between 25 mA SIR and 500 mA FBP global flow was -9.7%, 8.8%, -3.1%, and 26.4%. The average variability of flow measurements in a nonoccluded region was 16.3%, 24.1%, and 937.9% for the 500 mA FBP, 25 mA SIR, and 25 mA FBP, respectively. In numerical simulations, SIR mitigated streak artifacts in the low dose data and yielded flow maps with mean error <7% and standard deviation <9% of mean, for 30 × 30 pixel ROIs (12.9 × 12.9 mm(2)). In comparison, low dose FBP flow errors were -38% to +258%, and standard deviation was 6%-93%. Additionally, low dose SIR achieved 4.6 times improvement in flow map CNR(2) per unit input dose compared to low dose FBP. SIR reconstruction can reduce image noise and mitigate streaking artifacts caused by photon starvation in dynamic CT myocardial perfusion data sets acquired at low dose (low tube current), and improve perfusion map quality in comparison to FBP reconstruction at the same dose.