Efficient implementation of a filtered back-projection algorithm using a voxel-by-voxel approach

The large amount of image data necessary for high-resolution 3D reconstruction of macromolecular assemblies leads to significant increases in the computational time. One of the most time consuming operations is 3D density map reconstruction, and software optimization can greatly reduce the time required for any given structural study. The majority of algorithms proposed for improving the computational effectiveness of a 3D reconstruction are based on a ray-by-ray projection of each image into the reconstructed volume. In this paper, we propose a novel fast implementation of the "filtered back-projection" algorithm based on a voxel-by-voxel principle. Our version of this implementation has been exhaustively tested using both model and real data. We compared 3D reconstructions obtained by the new approach with results obtained by the filtered Back-Projections algorithm and the Fourier-Bessel algorithm commonly used for reconstructing icosahedral viruses. These computational experiments demonstrate the robustness, reliability, and efficiency of this approach.     

A Novel Iterative CT Reconstruction Approach Based on FBP Algorithm

The Filtered Back-Projection (FBP) algorithm and its modified versions are the most important techniques for CT (Computerized tomography) reconstruction, however, it may produce aliasing degradation in the reconstructed images due to projection discretization. The general iterative reconstruction (IR) algorithms suffer from their heavy calculation burden and other drawbacks. In this paper, an iterative FBP approach is proposed to reduce the aliasing degradation. In the approach, the image reconstructed by FBP algorithm is treated as the intermediate image and projected along the original projection directions to produce the reprojection data. The difference between the original and reprojection data is filtered by a special digital filter, and then is reconstructed by FBP to produce a correction term. The correction term is added to the intermediate image to update it. This procedure can be performed iteratively to improve the reconstruction performance gradually until certain stopping criterion is satisfied. Some simulations and tests on real data show the proposed approach is better than FBP algorithm or some IR algorithms in term of some general image criteria. The calculation burden is several times that of FBP, which is much less than that of general IR algorithms and acceptable in the most situations. Therefore, the proposed algorithm has the potential applications in practical CT systems.     

Statistical learning methods as a preprocessing step for survival analysis: evaluation of concept using lung cancer data

Background

Despite its superb lateral resolution, flat-panel-detector (FPD) based tomosynthesis suffers from low contrast and inter-plane artifacts caused by incomplete cancellation of the projection components stemming from outside the focal plane. The incomplete cancellation of the projection components, mostly due to the limited scan angle in the conventional tomosynthesis scan geometry, often makes the image contrast too low to differentiate the malignant tissues from the background tissues with confidence.

Methods

In this paper, we propose a new method to suppress the inter-plane artifacts in FPD-based tomosynthesis. If 3D whole volume CT images are available before the tomosynthesis scan, the CT image data can be incorporated into the tomosynthesis image reconstruction to suppress the inter-plane artifacts, hence, improving the image contrast. In the proposed technique, the projection components stemming from outside the region-of-interest (ROI) are subtracted from the measured tomosynthesis projection data to suppress the inter-plane artifacts. The projection components stemming from outside the ROI are calculated from the 3D whole volume CT images which usually have lower lateral resolution than the tomosynthesis images. The tomosynthesis images are reconstructed from the subtracted projection data which account for the x-ray attenuation through the ROI. After verifying the proposed method by simulation, we have performed both CT scan and tomosynthesis scan on a phantom and a sacrificed rat using a FPD-based micro-CT.

Results

We have measured contrast-to-noise ratio (CNR) from the tomosynthesis images which is an indicator of the residual inter-plane artifacts on the focal-plane image. In both cases of the simulation and experimental imaging studies of the contrast evaluating phantom, CNRs have been significantly improved by the proposed method. In the rat imaging also, we have observed better visual contrast from the tomosynthesis images reconstructed by the proposed method.

Conclusions

The proposed tomosynthesis technique can improve image contrast with aids of 3D whole volume CT images. Even though local tomosynthesis needs extra 3D CT scanning, it may find clinical applications in special situations in which extra 3D CT scan is already available or allowed.     

Simulation of scanner- and patient-specific low-dose CT imaging from existing CT images

PurposeSimulating low-dose Computed Tomography (CT) facilitates in-silico studies into the required dose for a diagnostic task. Conventionally, low-dose CT images are created by adding noise to the projection data. However, in practice the raw data is often simply not available. This paper presents a new method for simulating patient-specific, low-dose CT images without the need of the original projection data.MethodsThe low-dose CT simulation method included the following: (1) computation of a virtual sinogram from a high dose CT image through a radon transform; (2) simulation of a ‘reduced’-dose sinogram with appropriate amounts of noise; (3) subtraction of the high-dose virtual sinogram from the reduced-dose sinogram; (4) reconstruction of a noise volume via filtered back-projection; (5) addition of the noise image to the original high-dose image. The required scanner-specific parameters, such as the apodization window, bowtie filter, the X-ray tube output parameter (reflecting the photon flux) and the detector read-out noise, were retrieved from calibration images of a water cylinder. The low-dose simulation method was evaluated by comparing the noise characteristics in simulated images with experimentally acquired data.ResultsThe models used to recover the scanner-specific parameters fitted accurately to the calibration data, and the values of the parameters were comparable to values reported in literature. Finally, the simulated low-dose images accurately reproduced the noise characteristics in experimentally acquired low-dose-volumes.ConclusionThe developed methods truthfully simulate low-dose CT imaging for a specific scanner and reconstruction using filtered backprojection. The scanner-specific parameters can be estimated from calibration data.     

An iterative deconvolution algorithm for image recovery in clinical CT: A phantom study

PurposeTo study the feasibility of using an iterative reconstruction algorithm to improve previously reconstructed CT images which are judged to be non-diagnostic on clinical review. A novel rapidly converging, iterative algorithm (RSEMD) to reduce noise as compared with standard filtered back-projection algorithm has been developed.Materials and methodsThe RSEMD method was tested on in-silico, Catphan^®500, and anthropomorphic 4D XCAT phantoms. The method was applied to noisy CT images previously reconstructed with FBP to determine improvements in SNR and CNR. To test the potential improvement in clinically relevant CT images, 4D XCAT phantom images were used to simulate a small, low contrast lesion placed in the liver.ResultsIn all of the phantom studies the images proved to have higher resolution and lower noise as compared with images reconstructed by conventional FBP. In general, the values of SNR and CNR reached a plateau at around 20 iterations with an improvement factor of about 1.5 for in noisy CT images. Improvements in lesion conspicuity after the application of RSEMD have also been demonstrated. The results obtained with the RSEMD method are in agreement with other iterative algorithms employed either in image space or with hybrid reconstruction algorithms.ConclusionsIn this proof of concept work, a rapidly converging, iterative deconvolution algorithm with a novel resolution subsets-based approach that operates on DICOM CT images has been demonstrated. The RSEMD method can be applied to sub-optimal routine-dose clinical CT images to improve image quality to potentially diagnostically acceptable levels.     

Enhancement of soft-tissue contrast in cone-beam CT using an anti-scatter grid with a sparse sampling approach

PurposeAnti-scatter grids suppress the scatter substantially thus improving image contrast in radiography. However, its active use in cone-beam CT for the purpose of improving contrast-to-noise ratio (CNR) has not been successful mainly due to the increased noise related to Poisson statistics of photons. This paper proposes a sparse-view scanning approach to address the above issue.MethodCompared to the conventional cone-beam CT imaging framework, the proposed method reduces the number of projections and increases exposure in each projection to enhance image quality without an additional cost of radiation dose to patients. For image reconstruction from sparse-view data, an adaptive-steepest-descent projection-onto-convex-sets (ASD POCS) algorithm regularized by total-variation (TV) minimization was adopted. Contrast and CNR with various scattering conditions were evaluated in projection domain by a simulation study using GATE. Then we evaluated contrast, resolution, and image uniformity in CT image domain with Catphan phantom. A head phantom with soft-tissue structures was also employed for demonstrating a realistic application. A virtual grid-based estimation and reduction of scatter has also been implemented for comparison with the real anti-scatter grid.ResultsIn the projection domain evaluation, contrast and CNR enhancement was observed when using an anti-scatter grid compared to the virtual grid. In the CT image domain, the proposed method produced substantially higher contrast and CNR of the low-contrast structures with much improved image uniformity.ConclusionWe have shown that the proposed method can provide high-quality CBCT images particularly with an increased contrast of soft-tissue at a neutral dose for image-guidance.     

A Novel Weighted Total Difference Based Image Reconstruction Algorithm for Few-View Computed Tomography

In practical applications of computed tomography (CT) imaging, due to the risk of high radiation dose imposed on the patients, it is desired that high quality CT images can be accurately reconstructed from limited projection data. While with limited projections, the images reconstructed often suffer severe artifacts and the edges of the objects are blurred. In recent years, the compressed sensing based reconstruction algorithm has attracted major attention for CT reconstruction from a limited number of projections. In this paper, to eliminate the streak artifacts and preserve the edge structure information of the object, we present a novel iterative reconstruction algorithm based on weighted total difference (WTD) minimization, and demonstrate the superior performance of this algorithm. The WTD measure enforces both the sparsity and the directional continuity in the gradient domain, while the conventional total difference (TD) measure simply enforces the gradient sparsity horizontally and vertically. To solve our WTD-based few-view CT reconstruction model, we use the soft-threshold filtering approach. Numerical experiments are performed to validate the efficiency and the feasibility of our algorithm. For a typical slice of FORBILD head phantom, using 40 projections in the experiments, our algorithm outperforms the TD-based algorithm with more than 60% gains in terms of the root-mean-square error (RMSE), normalized root mean square distance (NRMSD) and normalized mean absolute distance (NMAD) measures and with more than 10% gains in terms of the peak signal-to-noise ratio (PSNR) measure. While for the experiments of noisy projections, our algorithm outperforms the TD-based algorithm with more than 15% gains in terms of the RMSE, NRMSD and NMAD measures and with more than 4% gains in terms of the PSNR measure. The experimental results indicate that our algorithm achieves better performance in terms of suppressing streak artifacts and preserving the edge structure information of the object.     

Three-dimensional reconstruction of cytochrome oxidase vesicle crystals prepared by cholate solubilization

Cytochrome oxidase vesicle crystals with long-range order have been obtained from cholate-solubilized, highly purified reconstitutively active preparations. These crystals, which are suitable for electron-microscopic structure investigation, show pgg symmetry in the 0 degree projection. Using Fourier reconstruction and modified back-projection methods, a three-dimensional reconstruction has been obtained at a resolution of 25 A. Our structural results are in agreement with the model of Henderson et al. [J. Mol. Biol. 112, 631 (1977)] obtained for their Triton-derived crystals.     

A model-based parallel origin and orientation refinement algorithm for cryoTEM and its application to the study of virus structures

We present a model-based parallel algorithm for origin and orientation refinement for 3D reconstruction in cryoTEM. The algorithm is based upon the Projection Theorem of the Fourier Transform. Rather than projecting the current 3D model and searching for the best match between an experimental view and the calculated projections, the algorithm computes the Discrete Fourier Transform (DFT) of each projection and searches for the central section ("cut") of the 3D DFT that best matches the DFT of the projection. Factors that affect the efficiency of a parallel program are first reviewed and then the performance and limitations of the proposed algorithm are discussed. The parallel program that implements this algorithm, called PO(2)R, has been used for the refinement of several virus structures, including those of the 500 Angstroms diameter dengue virus (to 9.5 Angstroms resolution), the 850 Angstroms mammalian reovirus (to better than 7A), and the 1800 Angstroms paramecium bursaria chlorella virus (to 15 Angstroms).     

System Matrix Analysis for Computed Tomography Imaging

In practical applications of computed tomography imaging (CT), it is often the case that the set of projection data is incomplete owing to the physical conditions of the data acquisition process. On the other hand, the high radiation dose imposed on patients is also undesired. These issues demand that high quality CT images can be reconstructed from limited projection data. For this reason, iterative methods of image reconstruction have become a topic of increased research interest. Several algorithms have been proposed for few-view CT. We consider that the accurate solution of the reconstruction problem also depends on the system matrix that simulates the scanning process. In this work, we analyze the application of the Siddon method to generate elements of the matrix and we present results based on real projection data.     

First application of the GPU-based software framework TIGRE for proton CT image reconstruction

In proton therapy, the knowledge of the proton stopping power, i.e. the energy deposition per unit length within human tissue, is essential for accurate treatment planning. One suitable method to directly measure the stopping power is proton computed tomography (pCT). Due to the proton interaction mechanisms in matter, pCT image reconstruction faces some challenges: the unique path of each proton has to be considered separately in the reconstruction process adding complexity to the reconstruction problem. This study shows that the GPU-based open-source software toolkit TIGRE, which was initially intended for X-ray CT reconstruction, can be applied to the pCT image reconstruction problem using a straight line approach for the proton path. This simplified approach allows for reconstructions within seconds.To validate the applicability of TIGRE to pCT, several Monte Carlo simulations modeling a pCT setup with two Catphan® modules as phantoms were performed. Ordered-Subset Simultaneous Algebraic Reconstruction Technique (OS-SART) and Adaptive-Steepest-Descent Projection Onto Convex Sets (ASD-POCS) were used for image reconstruction. Since the accuracy of the approach is limited by the straight line approximation of the proton path, requirements for further improvement of TIGRE for pCT are addressed.     

Iterative Image Reconstruction for Sparse-View CT Using Normal-Dose Image Induced Total Variation Prior

X-ray computed tomography (CT) iterative image reconstruction from sparse-view projection data has been an important research topic for radiation reduction in clinic. In this paper, to relieve the requirement of misalignment reduction operation of the prior image constrained compressed sensing (PICCS) approach introduced by Chen et al, we present an iterative image reconstruction approach for sparse-view CT using a normal-dose image induced total variation (ndiTV) prior. The associative objective function of the present approach is constructed under the penalized weighed least-square (PWLS) criteria, which contains two terms, i.e., the weighted least-square (WLS) fidelity and the ndiTV prior, and is referred to as “PWLS-ndiTV”. Specifically, the WLS fidelity term is built based on an accurate relationship between the variance and mean of projection data in the presence of electronic background noise. The ndiTV prior term is designed to reduce the influence of the misalignment between the desired- and prior- image by using a normal-dose image induced non-local means (ndiNLM) filter. Subsequently, a modified steepest descent algorithm is adopted to minimize the associative objective function. Experimental results on two different digital phantoms and an anthropomorphic torso phantom show that the present PWLS-ndiTV approach for sparse-view CT image reconstruction can achieve noticeable gains over the existing similar approaches in terms of noise reduction, resolution-noise tradeoff, and low-contrast object detection.     

CT iterative reconstruction in image space: A phantom study

Although iterative reconstruction is widely applied in SPECT/PET, its introduction in clinical CT is quite recent, in the past the demand for extensive computer power and long image reconstruction times have stopped the diffusion of this technique. Recently Iterative Reconstruction in Image Space (IRIS) has been introduced on Siemens top CT scanners. This recon method works on image data area, reducing the time-consuming loops on raw data and noise removal is obtained in subsequent iterative steps with a smoothing process. We evaluated image noise, low contrast resolution, CT number linearity and accuracy, transverse and z-axis spatial resolution using some dedicated phantoms in single, dual source and cardiac mode. We reconstructed images with a traditional filtered back-projection algorithm and with IRIS. The iterative procedure preserves spatial resolution, CT number accuracy and linearity moreover decreases image noise. These preliminary results support the idea that dose reduction with preserved image quality is possible with IRIS, even if studies on patients are necessary to confirm these data.     

Artificial intelligence in image reconstruction: The change is here

Innovations in CT have been impressive among imaging and medical technologies in both the hardware and software domain. The range and speed of CT scanning improved from the introduction of multidetector-row CT scanners with wide-array detectors and faster gantry rotation speeds. To tackle concerns over rising radiation doses from its increasing use and to improve image quality, CT reconstruction techniques evolved from filtered back projection to commercial release of iterative reconstruction techniques, and recently, of deep learning (DL)-based image reconstruction. These newer reconstruction techniques enable improved or retained image quality versus filtered back projection at lower radiation doses. DL can aid in image reconstruction with training data without total reliance on the physical model of the imaging process, unique artifacts of PCD-CT due to charge sharing, K-escape, fluorescence x-ray emission, and pulse pileups can be handled in the data-driven fashion. With sufficiently reconstructed images, a well-designed network can be trained to upgrade image quality over a practical/clinical threshold or define new/killer applications. Besides, the much smaller detector pixel for PCD-CT can lead to huge computational costs with traditional model-based iterative reconstruction methods whereas deep networks can be much faster with training and validation. In this review, we present techniques, applications, uses, and limitations of deep learning-based image reconstruction methods in CT.     

Coral surface area quantification–evaluation of established techniques by comparison with computer tomography

The surface area of scleractinian corals represents an important reference parameter required for various aspects of coral reef science. However, with advancements in detection accuracy and novel approaches for coral surface area quantification, evaluation of established techniques in comparison with state-of-the-art technology gains importance to coral researchers. This study presents an evaluation of methodological accuracy for established techniques in comparison to a novel approach composed of computer tomography (CT) and 3-dimensional surface reconstruction. The skeleton surface area of reef corals from six genera representing the most common morphological growth forms was acquired by CT and subsequently measured by computer-aided 3-dimensional surface reconstruction. Surface area estimates for the same corals were also obtained by application of four established techniques: Simple and Advanced Geometry, Wax Coating and Planar Projection Photography. Comparison of the resulting area values revealed significant differences between the majority (82%) of established techniques and the CT reference. Genus-specific analysis assigned the highest accuracy to geometric approximations (Simple or Advanced Geometry) for the majority of assessed coral genera (maximum accuracy: 104%; Simple Geometry with Montipora sp.). The commonly used and invasive Wax Coating technique reached intermediate accuracy (47–74%) for the majority of genera, but performed outstanding in the measurement of branching Acropora spp. corals (maximum accuracy: 101%), while the Planar Projection Photography delivered genera-wide low accuracy (12–36%). Comparison of area values derived from established techniques and CT additionally yielded approximation factors (AFs) applicable as factors in the mathematical improvement of surface area estimates by established techniques in relation to CT reference accuracy. Communicated by Geology Editor Dr Bernhard Riegl     

Electrical impedance tomography via filtered-back projection of fan current distribution: a numerical simulation

An approach to electrical impedance tomography (EIT) data acquisition inspired by NMR-filtered back-projection imaging with fan isochromat distribution is proposed. A current projection is generated by injecting current at a certain point of the sample and simultaneously collecting the current itself at different points on the half space opposite the point of current injection. After that, the injection is shifted to another point and collected as above and so on. A very simple algebra and software support the numerical simulations. This method is expected to be more sensitive than the traditional method based on potential measurements. A preliminary low resolution experiment is presented.     

基于投影寻踪法的武汉市“两型社会”评价模型与实证研究

为克服现有“两型社会”评价中存在的主观性强、不易处理高维数据等缺陷,提出了基于投影寻踪法的武汉市“两型社会”评价新方法。从资源、环境、经济、社会四个子系统出发,构建了武汉市"两型社会"评价指标体系;选取武汉市2000-2009年数据作为样本,将多维评价指标值投影为一维投影数据;引入加速遗传算法,优化投影指标函数寻求最佳投影方向;根据投影值大小对武汉市2000-2009年“两型社会”发展状况进行比较,利用最佳投影方向信息研究了各个指标对武汉市”两型社会“发展的影响程度。研究结果表明,2000-2009年,武汉市“两型社会”建设呈现出良好的发展态势,建成区绿化覆盖率、人均公共绿地面积、第三产业增加值占GDP比重、空气质量优良率、每千人口医院床位数、工业用水重复利用率、每万人在校大学生人数、单位GDP能耗、每万人拥有公共交通车辆等指标是武汉市“两型社会”建设的重要驱动因素。对此就武汉市建设“两型社会”提出了对策和建议。最后,指出投影寻踪模型为城市"两型社会"发展综合评价提供了一种值得探索和尝试的新方法。     

Electron tomography of amplified nanogold immunolabelling: Improvement of quality based on alignment of projections with sinograms and use of post-reconstruction deconvolution

Electron tomography of immunolabelled proteins identified with amplified nanogold particles imaged by Scanning and Transmission Electron Microscopy within thick sections is a powerful method to investigate the three-dimensional organization of complex cellular machineries. In order to increase the overall quality of the reconstructed cube, we have developed two methods that improve the tomographic reconstruction process. We first performed a very precise alignment of the projections before reconstruction with a technique using sinograms. After reconstruction, we propose to compute image restoration by calculating the Point Spread Function of the projection/back-projection system and to use it to deblur the reconstructed cubes. Improvement in the quality of the reconstructed cubes is demonstrated on images of nucleolar proteins tagged with EGFP and immunolabelled with nanogold particles.     

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ₁-regularized parallel imaging methods.     

Image reconstruction of optical computed tomography by using the algebraic reconstruction technique for dose readouts of polymer gel dosimeters

Optical computed tomography (optical CT) has been proven to be a useful tool for dose readouts of polymer gel dosimeters. In this study, the algebraic reconstruction technique (ART) for image reconstruction of gel dosimeters was used to improve the image quality of optical CT. Cylindrical phantoms filled with N-isopropyl-acrylamide polymer gels were irradiated using a medical linear accelerator. A circular dose distribution and a hexagonal dose distribution were produced by applying the VMAT technique and the six-field dose delivery, respectively. The phantoms were scanned using optical CT, and the images were reconstructed using the filtered back-projection (FBP) algorithm and the ART. For the circular dose distribution, the ART successfully reduced the ring artifacts and noise in the reconstructed image. For the hexagonal dose distribution, the ART reduced the hot spots at the entrances of the beams and increased the dose uniformity in the central region. Within 50% isodose line, the gamma pass rates for the 2 mm/3% criteria for the ART and FBP were 99.2% and 88.1%, respectively. The ART could be used for the reconstruction of optical CT images to improve image quality and provide accurate dose conversion for polymer gel dosimeters.