Computationally efficient filtered-backprojection algorithm for tomographic image reconstruction using Walsh transform

To investigate feasibility of applying deep learning image reconstruction (DLIR) algorithm in a low-kilovolt enhanced scan of the upper abdomen. A total of 64 patients (BMI<28) are selected for the enhanced upper abdomen scan and divided evenly into two groups. The tube voltages in Group A are 100kV in arterial phase and 80kV in venous phase, while tube voltages are 120kV during two phases in Group B. Image reconstruction algorithms used in Group A include the filtered back projection (FBP) algorithm, the adaptive statistical iterative reconstruction-Veo (ASIR-V 40% and 80%) algorithm, and the DLIR algorithm (DL-L, DL-M, DL-H). Image reconstruction algorithm used in Group B is ASIR-V40%. The different reconstruction algorithm images are used to measure the common hepatic artery, liver, renal cortex, erector spinae, and subcutaneous adipose in the arterial phase and the average CT value and standard deviation of the portal vein, liver, spleen, erector spinae, and subcutaneous adipose in the portal phase. The signal-to-noise ratio (SNR) is calculated, and the images are also scored subjectively. In Group A, noise in the aorta, liver, portal vein (the portal phase), spleen (the portal phase), renal cortex, retroperitoneal adipose, and muscle is significantly lower in both the DL-H and ASIR-V80% images, and the SNR is significantly higher than those in the remaining groups (P<0.05). The SNR of each tissue and organ in Group B is not significantly different from that in DL-M, DL-L, and ASIR-V40% in Group A (P>0.05). The subjective image quality scores in the DL-H and B groups are higher than those in the other groups, and the FBP group has significantly lower image quality than the remaining groups (P<0.05). For upper abdominal low-kilovolt enhanced scan data, the DLIR-H gear yields a more satisfactory image quality than the FBP and ASIR-V.

Digital breast tomosynthesis (DBT) is considered in clinics as a standard three-dimensional imaging modality, allowing the earlier detection of cancer. It typically acquires only 10–30 projections over a limited angle range of 15–60° with a stationary detector and typically uses a computationally-efficient filtered-backprojection (FBP) algorithm for image reconstruction. However, a common FBP algorithm yields poor image quality resulting from the loss of average image value and the presence of severe image artifacts due to the elimination of the dc component of the image by the ramp filter and to the incomplete data, respectively. As an alternative, iterative reconstruction methods are often used in DBT to overcome these difficulties, even though they are still computationally expensive. In this study, as a compromise, we considered a projection-angle-dependent filtering method in which one-dimensional geometry-adapted filter kernels are computed with the aid of a conjugate-gradient method and are incorporated into the standard FBP framework. We implemented the proposed algorithm and performed systematic simulation works to investigate the imaging characteristics. Our results indicate that the proposed method is superior to a conventional FBP method for DBT imaging and has a comparable computational cost, while preserving good image homogeneity and edge sharpening with no serious image artifacts.

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.

Low-dose computed tomography (CT) has attracted much attention in clinical applications since X-ray radiations can cause serious health risks to patients. Sparse-view CT imaging is one of the major ways to reduce radiation dose. However, if reconstructing the sparse-view CT images with conventional filtered backprojection (FBP) algorithm, image quality may be significantly degraded due to the severe streaking artifacts. Therefore, iterative sparse-view CT image reconstruction (IR) algorithms have been developed and utilized to improve image quality. One drawback of using the IR algorithms is they usually spend long computation time. Additionally, adjusting and optimizing the hyper-parameters that are needed during iteration procedures is also time-consuming, some- times may even depend on individual experience. These potential drawbacks strongly limit the wide applications of IR algorithms. Aiming at partially overcome such difficulties, in the present work, we propose a deep iterative reconstruction (DIR) framework to generalize the conventional IR algorithms by mapping them into the deep neural network (DNN) technique. With this proposed DIR algorithms, the prior term, the data fidelity term, and the hyper-parameters can all be represented and learned by network. By doing so, some generalized iterative models can be used to perform high quality sparse-view CT image reconstructions. Numerical experiments based on clinical patient data demonstrated that the proposed DIR algorithms can mitigate the streaking artifacts more effectively while well preserving the subtle structures.

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.

OA158] Noise equivalent number of quanta (NEQ): A tool for choosing the optimal reconstruction algorithm in computed tomography (CT)

Localizing and characterizing clinically-significant lung nodules, a potential precursor to lung cancer, at the lowest achievable radiation dose is demanded to minimize the stochastic radiation effects from x-ray computed tomography (CT). A minimal dose level is heavily dependent on the image reconstruction algorithms and clinical task, in which the tissue texture always plays an important role. This study aims to investigate the dependence through a task-based evaluation at multiple dose levels and variable textures in reconstructions with prospective patient studies. 133 patients with a suspicious pulmonary nodule scheduled for biopsy were recruited and the data was acquired at120kVp with three different dose levels of 100, 40 and 20mAs. Three reconstruction algorithms were implemented: analytical filtered back-projection (FBP) with optimal noise filtering; statistical Markov random field (MRF) model with optimal Huber weighting (MRF-H) for piecewise smooth reconstruction; and tissue-specific texture model (MRF-T) for texture preserved statistical reconstruction. Experienced thoracic radiologists reviewed and scored all images at random, blind to the CT dose and reconstruction algorithms. The radiologists identified the nodules in each image including the 133 biopsy target nodules and 66 other non-target nodules. For target nodule characterization, only MRF-T at 40mAs showed no statistically significant difference from FBP at 100mAs. For localizing both the target nodules and the non-target nodules, some as small as 3mm, MRF-T at 40 and 20mAs levels showed no statistically significant difference from FBP at 100mAs, respectively. MRF-H and FBP at 40 and 20mAs levels performed statistically differently from FBP at 100mAs. This investigation concluded that (1) the textures in the MRF-T reconstructions improves both the tasks of localizing and characterizing nodules at low dose CT and (2) the task of characterizing nodules is more challenging than the task of localizing nodules and needs more dose or enhanced textures from reconstruction.

Computed tomography perfusion (CTP) and computed tomography angiography (CTA) are valuable tools for diagnosing acute ischemic stroke (AIS). It is essential to obtain high-quality CTP and CTA images in short time. This study aimed to evaluate the image quality and diagnostic performance of brain CTP and CTA images generated from CTP reconstructed by a deep learning image reconstruction (DLIR) algorithm on patients with AIS. The study prospectively enrolled 54 patients with suspected AIS undergoing non-contrast CT and CTP within 24 hours. CTP datasets were reconstructed with three levels of adaptive statistical iterative reconstruction-Veo algorithm [ASIR-V 0% with filtered back projection (FBP), ASIR-V 40%, and ASIR-V 80%] and three levels of DLIR, including low (DLIR-L), medium (DLIR-M), and high (DLIR-H). CTA images were generated using the CTP datasets at the peak arterial phase. Objective parameters including signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and noise reduction rate. Subjective evaluation was assessed according to Abels scoring system. Perfusion parameters and detection accuracy for infarction core lesions were evaluated. The objective and subjective image quality of CTA images were also evaluated. All reconstructions produced similar CT values (P>0.05). With the increase of ASIR-V and DLIR reconstruction strength, image noise decreased, while SNR and CNR increased for CTP images, especially in white matter. DLIR-H, DLIR-M, and ASIR-V80% yielded higher subjective scores than did ASIR-V40% and FBP. DLIR-H provided the highest noise reduction rate and detection accuracy. No significant difference was found in conventional parameters, the volume of infarct core, or ischemic penumbra among the 6 groups (P>0.05). The objective evaluation of reconstructed CTA images was comparable in DLIR-H, DLIR-M, and ASIR-V80% (P>0.05). The subjective scores of the DLIR-H and DLIR-M images were higher than those of the other groups, especially ASIR-V40% and FBP (P<0.05). Compared with FBP and ASIR-V40%, DLIR-H, DLIR-M, and ASIR-V80% improved the overall image quality of CTP and CTA images to varying degrees. Furthermore, DLIR-H and DLIR-M showed the best performance. DLIR-H is the best choice in diagnosing AIS with improved detection accuracy for cerebral infarction. Reconstructing CTA images using CTP datasets could reduce contrast agent and radiation dose.

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

Sparse-view x-ray micro computed tomography (micro-CT) reconstruction algorithms via total variation (TV) optimize the data without introducing notable noise and artifacts, resulting in significant scanning time reduction while maintaining image quality. However, due to the piecewise constant assumption for the image, a conventional TV minimization often suffers from patchy artifacts in reconstructed images. Moreover, for lack of directional gradient in TV some directional information are lost. To obviate these drawbacks, in this study we develop a penalized weighted least-square (PWLS) strategy for micro-CT sparse-view image reconstruction by incorporating an adaptive weighted total variation in combination with an adaptive weighted diagonal total variation (AwTV+AwDTV) penalty term. The AwTV considers the vertical and horizontal gradients while the AwDTV uses the diagonal gradients. The associated weights which are defined based on the anisotropic edge properties of an image, are expressed as an exponential function and can be adaptively adjusted by the amount of the difference between voxel intensities to preserve the edge details. To evaluate the presented (AwTV+AwDTV)-PWLS algorithm, both qualitative and quantitative studies were performed by computer simulations and micro-CT data experiments. The Shepp-Logan phantom for computer simulation and the micro-CT water phantom and a rat skull for micro-CT experiments are employed to perform image reconstruction. To evaluate the performance of AwTV+AwDTV algorithm, we compared it with TV and AwTV reconstruction algorithms. The simulation results show that the presented (AwTV+AwDTV)-PWLS algorithm can achieve the lowest RMSE and highest PSNR, SSIM and MTF for different number of projections as compared to the AwTV and conventional TV algorithms. The micro-CT data results confirmed the superiority of the proposed (AwTV+AwDTV) method to the AwTV and TV methods for different number of projections.

Four-dimensional computed tomography (4DCT) has been widely used in cancer radiotherapy for accurate target delineation and motion measurement for tumors in the thorax and upper abdomen areas. However, its prolonged scanning duration causes a considerable increase of radiation dose compared to conventional CT, which is a major concern in its clinical application. This work is to develop a new algorithm to reconstruct 4DCT images from undersampled projections acquired at low mA s levels in order to reduce the imaging dose. Conventionally, each phase of 4DCT is reconstructed independently using the filtered backprojection (FBP) algorithm. The basic idea of the authors' new algorithm is that by utilizing the common information among different phases, the input information required to reconstruct the image of high quality, and thus the imaging dose, can be reduced. The authors proposed a temporal nonlocal means (TNLM) method to explore the interphase similarity. All phases of the 4DCT images are reconstructed simultaneously by minimizing a cost function consisting of a data fidelity term and a TNLM regularization term. The authors utilized a modified forward-backward splitting algorithm and a Gauss-Jacobi iteration method to efficiently solve the minimization problem. The algorithm was also implemented on a graphics processing unit (GPU) to improve the computational speed. The authors' reconstruction algorithm has been tested on a digital NCAT thorax phantom in three low dose scenarios: All projections with low mA s level, undersampled projections with high mA s level, and undersampled projections with low mA s level. In all three low dose scenarios, the new algorithm generates visually much better CT images containing less image noise and streaking artifacts compared to the standard FBP algorithm. Quantitative analysis shows that by comparing the authors' TNLM algorithm to the standard FBP algorithm, the contrast-to-noise ratio has been improved by a factor of 3.9-10.2 and the signal-to-noise ratio has been improved by a factor of 2.1-5.9, depending on the cases. In the situation of undersampled projection data, the majority of the streaks in the images reconstructed by FBP can be suppressed using the authors' algorithm. The total reconstruction time for all ten phases of a slice ranges from 40 to 90 s on an NVIDIA Tesla C1060 GPU card. The experimental results indicate that the authors' new algorithm outperforms the conventional FBP algorithm in effectively reducing the image artifacts due to undersampling and suppressing the image noise due to the low mA s level.

The authors studied certain characteristics of the expectation-maximization (EM) algorithm for image reconstruction in positron emission tomography (PET). They have attempted to speed up the algorithm by performing some time-consuming computation only once, at the initiation stage. They have studied the resulting memory size, disk space, and CPU requirements versus the number of pixels in the reconstructed image and the number of gamma -ray detectors in the tomograph. The convergence and image quality have been studied as a function of the number of iterations performed. Preliminary results are presented. >

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.

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.