Low-dose CT reconstruction via edge-preserving total variation regularization

High radiation dose in computed tomography (CT) scans increases the lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with total variation (TV) regularization have been developed to reconstruct CT images from highly undersampled data acquired at low mAs levels in order to reduce the imaging dose. Nonetheless, the low-contrast structures tend to be smoothed out by the TV regularization, posing a great challenge for the TV method. To solve this problem, in this work we develop an iterative CT reconstruction algorithm with edge-preserving TV (EPTV) regularization to reconstruct CT images from highly undersampled data obtained at low mAs levels. The CT image is reconstructed by minimizing energy consisting of an EPTV norm and a data fidelity term posed by the x-ray projections. The EPTV term is proposed to preferentially perform smoothing only on the non-edge part of the image in order to better preserve the edges, which is realized by introducing a penalty weight to the original TV norm. During the reconstruction process, the pixels at the edges would be gradually identified and given low penalty weight. Our iterative algorithm is implemented on graphics processing unit to improve its speed. We test our reconstruction algorithm on a digital NURBS-based cardiac-troso phantom, a physical chest phantom and a Catphan phantom. Reconstruction results from a conventional filtered backprojection (FBP) algorithm and a TV regularization method without edge-preserving penalty are also presented for comparison purposes. The experimental results illustrate that both the TV-based algorithm and our EPTV algorithm outperform the conventional FBP algorithm in suppressing the streaking artifacts and image noise under a low-dose context. Our edge-preserving algorithm is superior to the TV-based algorithm in that it can preserve more information of low-contrast structures and therefore maintain acceptable spatial resolution.     

GPU-based iterative cone-beam CT reconstruction using tight frame regularization

The x-ray imaging dose from serial cone-beam computed tomography (CBCT) scans raises a clinical concern in most image-guided radiation therapy procedures. It is the goal of this paper to develop a fast graphic processing unit (GPU)-based algorithm to reconstruct high-quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose. For this purpose, we have developed an iterative tight-frame (TF)-based CBCT reconstruction algorithm. A condition that a real CBCT image has a sparse representation under a TF basis is imposed in the iteration process as regularization to the solution. To speed up the computation, a multi-grid method is employed. Our GPU implementation has achieved high computational efficiency and a CBCT image of resolution 512 × 512 × 70 can be reconstructed in ～5 min. We have tested our algorithm on a digital NCAT phantom and a physical Catphan phantom. It is found that our TF-based algorithm is able to reconstruct CBCT in the context of undersampling and low mAs levels. We have also quantitatively analyzed the reconstructed CBCT image quality in terms of the modulation-transfer function and contrast-to-noise ratio under various scanning conditions. The results confirm the high CBCT image quality obtained from our TF algorithm. Moreover, our algorithm has also been validated in a real clinical context using a head-and-neck patient case. Comparisons of the developed TF algorithm and the current state-of-the-art TV algorithm have also been made in various cases studied in terms of reconstructed image quality and computation efficiency.     

Higher order total variation regularization for EIT reconstruction

Electrical impedance tomography (EIT) attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. This is an ill-posed inverse problem; its solution is very unstable. Total variation (TV) regularization is one of the techniques commonly employed to stabilize reconstructions. However, it is well known that TV regularization induces staircase effects, which are not realistic in clinical applications. To reduce such artifacts, modified TV regularization terms considering a higher order differential operator were developed in several previous studies. One of them is called total generalized variation (TGV) regularization. TGV regularization has been successively applied in image processing in a regular grid context. In this study, we adapted TGV regularization to the finite element model (FEM) framework for EIT reconstruction. Reconstructions using simulation and clinical data were performed. First results indicate that, in comparison to TV regularization, TGV regularization promotes more realistic images.

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Graphical abstract Reconstructed conductivity changes located on selected vertical lines. For each of the reconstructed images as well as the ground truth image, conductivity changes located along the selected left and right vertical lines are plotted. In these plots, the notation GT in the legend stands for ground truth, TV stands for total variation method, and TGV stands for total generalized variation method. Reconstructed conductivity distributions from the GREIT algorithm are also demonstrated.

     

Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT

Flat-panel-detector x-ray cone-beam computed tomography (CBCT) is used in a rapidly increasing host of imaging applications, including image-guided surgery and radiotherapy. The purpose of the work is to investigate and evaluate image reconstruction from data collected at projection views significantly fewer than what is used in current CBCT imaging. Specifically, we carried out imaging experiments using a bench-top CBCT system that was designed to mimic imaging conditions in image-guided surgery and radiotherapy; we applied an image reconstruction algorithm based on constrained total-variation (TV)-minimization to data acquired with sparsely sampled view-angles and conducted extensive evaluation of algorithm performance. Results of the evaluation studies demonstrate that, depending upon scanning conditions and imaging tasks, algorithms based on constrained TV-minimization can reconstruct images of potential utility from a small fraction of the data used in typical, current CBCT applications. A practical implication of the study is that the optimization of algorithm design and implementation can be exploited for considerably reducing imaging effort and radiation dose in CBCT.     

Truncation artifact suppression in cone-beam radionuclide transmission CT using maximum likelihood techniques: evaluation with human subjects.

Transverse image truncation can be a serious problem for human imaging using cone-beam transmission CT (CB-CT) implemented on a conventional rotating gamma camera. If this problem can be solved, CB-CT will be useful for attenuation compensation of SPECT images. This paper presents a reconstruction method to reduce or eliminate the artifacts resulting from the truncation. The method uses a previously published transmission maximum likelihood EM algorithm, adapted to the cone-beam geometry. The reconstruction method is evaluated qualitatively using three human subjects of various dimensions and various degrees of truncation. For the two smaller subjects, with moderate truncation, the maximum likelihood method is very successful, nearly eliminating the artifacts seen with conventional filtered backprojection of truncated geometries. The use of an expanded reconstructed space, which contains the entire transverse slice of the subject, is necessary for optimal truncation removal. For the largest subject investigated, the truncation was substantial, and the artifacts were only partially removed by the maximum likelihood reconstruction. Nonetheless, the images were qualitatively superior to those obtained with filtered backprojection. An added elliptical support prior moderately increased the rate of convergence, and helped to force a reasonable body contour.     

低剂量CT的加权总变差重建算法

针对稀疏投影角度的CT图像重建问题,结合压缩感知理论,提出基于加权迭代支持检测的分块代数重建算法,以较少的投影角度重建出理想的CT图像。首先,针对传统的代数重建技术计算量大、收敛速度慢的问题,提出分块代数重建算法;其次,传统的最小总变差模型会引起图像过度平滑及纹理细节模糊等问题,对此提出一种最小加权总变差算法,即加权迭代支持检测算法,并建立加权迭代支持检测模型;最后,分块代数重建技术与加权迭代支持检测模型交替迭代,使重建结果趋于收敛。本文采用经典的Shepp-Logan体模及实际的脑部CT切片进行重建,以均方根误差作为重建图像的质量评判标准,并与其他重建算法的重建结果进行对比。在经过一定次数的迭代后,基于本文算法的重建图像更贴近原始图像,而且比其他算法更早收敛。实验结果表明,本文算法在重建质量及收敛速度上都优于其他对比算法。     

Aperture weighted cardiac reconstruction for cone-beam CT

Multi-row detectors together with fast rotating gantries made cardiac imaging possible for CT. Due to the cardiac motion, ECG gating has to be integrated into the reconstruction of the data measured on a low pitch helical trajectory. Since the first multi-row scanners were introduced, it has been shown that approximative true cone-beam reconstruction methods are most suitable for the task of retrospectively gated cardiac volume CT. In this paper, we present the aperture weighted cardiac reconstruction (AWCR), which is a three-dimensional reconstruction algorithm of the filtered back-projection type. It is capable of handling all illumination intervals of an object point, which occur as a consequence of a low pitch helical cone-beam acquisition. Therefore, this method is able to use as much redundant data as possible, resulting in an improvement of the image homogeneity, the signal to noise ratio and the temporal resolution. Different optimization techniques like the heart rate adaptive cardiac weighting or the automatic phase determination can be adopted to AWCR. The excellent image quality achieved by AWCR is presented for medical datasets acquired with both a 40-slice and a 64-slice cone-beam CT scanner.     

Cardiac cone-beam CT volume reconstruction using ART

Modern computed tomography systems allow volume imaging of the heart. Up to now, approximately two-dimensional (2D) and 3D algorithms based on filtered backprojection are used for the reconstruction. These algorithms become more sensitive to artifacts when the cone angle of the x-ray beam increases as it is the current trend of computed tomography (CT) technology. In this paper, we investigate the potential of iterative reconstruction based on the algebraic reconstruction technique (ART) for helical cardiac cone-beam CT. Iterative reconstruction has the advantages that it takes the cone angle into account exactly and that it can be combined with retrospective cardiac gating fairly easily. We introduce a modified ART algorithm for cardiac CT reconstruction. We apply it to clinical cardiac data from a 16-slice CT scanner and compare the images to those obtained with a current analytical reconstruction method. In a second part, we investigate the potential of iterative reconstruction for a large area detector with 256 slices. For the clinical cases, iterative reconstruction produces excellent images of diagnostic quality. For the large area detector, iterative reconstruction produces images superior to analytical reconstruction in terms of cone-beam artifacts.     

Chord-based image reconstruction in cone-beam CT with a curved detector

Modern computed tomography (CT) scanners use cone-beam configurations for increasing volume coverage, improving x-ray-tube utilization, and yielding isotropic spatial resolution. Recently, there have been significant developments in theory and algorithms for exact image reconstruction from cone-beam projections. In particular, algorithms have been proposed for image reconstruction on chords; and advantages over the existing algorithms offered by the chord-based algorithms include the high flexibility of exact image reconstruction for general scanning trajectories and the capability of exact reconstruction of images within a region of interest from truncated data. These chord-based algorithms have been developed only for flat-panel detectors. Many cone-beam CT scanners employ curved detectors for important practical considerations. Therefore, in this work, we have derived chord-based algorithms for a curved detector so that they can be applied to reconstructing images directly from data acquired by use of a CT scanner with a curved detector. We have also conducted preliminary numerical studies to demonstrate and evaluate the reconstruction properties of the derived chord-based algorithms for curved detectors.     

3D cone-beam CT reconstruction for circular trajectories

3D reconstruction from 2D projections obtained along a single circular source trajectory is most commonly done using an algorithm due to Feldkamp, Davis and Kress. In this paper we propose an alternative approach based on a cone-beam to parallel-beam rebinning step, a corresponding rebinning step into a rectangular virtual detector plane and a filtered backprojection. This approach yields an improved image quality reflected by a decreased low-intensity drop which is well known for 3D reconstruction from projection data obtained along circular trajectories. At the same time the computational complexity is lower than in Feldkamp's original approach. Based on this idea, a hybrid 3D cone-beam reconstruction method is formulated that enlarges the reconstruction volume in its dimension along the rotation axis of the cone-beam CT system. This enlargement is achieved by applying different reconstruction conditions for each voxel. An optimal ratio between the reconstructible and irradiated volume of the scanned object is achieved.     

Feldkamp-based cone-beam reconstruction for gantry-tilted helical multislice CT

Depending on the clinical application, it is frequently necessary to tilt the gantry of an x-ray CT system with respect to the patient and couch. For single-slice fan-beam systems, tilting the gantry introduces no errors or artifacts. Most current systems, however, are helical multislice systems with up to 16 slices. The multislice helical reconstruction algorithms used to create CT images must be modified to account for tilting of the gantry. If they are not, the quality of reconstructed images will be poor with the presence of significant artifacts, such as smearing and double-imaging of anatomical structures. Current CT systems employ three primary types of reconstruction algorithms: helical fan-beam approximation, advanced single-slice rebinning, and Feldkamp-based algorithms. This paper presents a generalized helical cone-beam Feldkamp-based algorithm that is valid for both tilted and nontilted orientations of the gantry. Unlike some of the other algorithms, generalization of the Feldkamp algorithm to include gantry tilt is simple and straightforward with no significant increase in computational complexity. The effect of gantry tilt for helical Feldkamp reconstruction is to introduce a lateral shift in the isocenter of the reconstructed slice of interest, which is a function of the tilt, couch speed, and view angle. The lateral shift is easily calculated and incorporated into the helical Feldkamp backprojection algorithm. A tilt-generalized helical Feldkamp algorithm has been developed and incorporated into Aquilion 16-slice CT (Toshiba, Japan) scanners. This paper describes modifications necessary for the tilt generalization and its verification.     

A combination-weighted Feldkamp-based reconstruction algorithm for cone-beam CT

The combination-weighted Feldkamp algorithm (CW-FDK) was developed and tested in a phantom in order to reduce cone-beam artefacts and enhance cranio-caudal reconstruction coverage in an attempt to improve image quality when utilizing cone-beam computed tomography (CBCT). Using a 256-slice cone-beam CT (256CBCT), image quality (CT-number uniformity and geometrical accuracy) was quantitatively evaluated in phantom and clinical studies, and the results were compared to those obtained with the original Feldkamp algorithm. A clinical study was done in lung cancer patients under breath holding and free breathing. Image quality for the original Feldkamp algorithm is degraded at the edge of the scan region due to the missing volume, commensurate with the cranio-caudal distance between the reconstruction and central planes. The CW-FDK extended the reconstruction coverage to equal the scan coverage and improved reconstruction accuracy, unaffected by the cranio-caudal distance. The extended reconstruction coverage with good image quality provided by the CW-FDK will be clinically investigated for improving diagnostic and radiotherapy applications. In addition, this algorithm can also be adapted for use in relatively wide cone-angle CBCT such as with a flat-panel detector CBCT.     

Artifact analysis of approximate helical cone-beam CT reconstruction algorithms

In this paper, four approximate cone-beam CT reconstruction algorithms are compared: Advanced single slice rebinning (ASSR) as a representative of algorithms employing a two dimensional approximation, PI, PI-SLANT, and 3-PI which all use a proper three dimensional back-projection. A detailed analysis of the image artifacts produced by these techniques shows that aliasing in the z-direction is the predominant source of artifacts for a 16-row scanner with 1.25 mm nominal slice thickness. For a detector with isotropic resolution of 0.5 mm, we found that ASSR and PI produce different kinds of artifacts which are almost at the same level, while PI-SLANT produces none of these artifacts. It is shown that the use of redundant data in the 3-PI method suppresses aliasing artifacts efficiently for both scanners.     

Motion-compensated iterative cone-beam CT image reconstruction with adapted blobs as basis functions

This paper presents a three-dimensional method to reconstruct moving objects from cone-beam X-ray projections using an iterative reconstruction algorithm and a given motion vector field. For the image representation, adapted blobs are used, which can be implemented efficiently as basis functions. Iterative reconstruction requires the calculation of line integrals (forward projections) through the image volume, which are compared with the actual measurements to update the image volume. In the existence of a divergent motion vector field, a change in the volumes of the blobs has to be taken into account in the forward and backprojections. An efficient method to calculate the line integral through the adapted blobs is proposed. It solves the problem, how to compensate for the divergence in the motion vector field on a grid of basis functions. The method is evaluated on two phantoms, which are subject to three different known motions. Moreover, a motion-compensated filtered back-projection reconstruction method is used, and the reconstructed images are compared. Using the correct motion vector field with the iterative motion-compensated reconstruction, sharp images are obtained, with a quality that is significantly better than gated reconstructions.     

Exact reconstruction of volumetric images in reverse helical cone-beam CT

Helical scanning configuration has been used widely in diagnostic cone-beam computed tomography (CBCT) for acquiring data sufficient for exact image reconstruction over an extended volume. In image-guided radiation therapy (IGRT) and other applications of CBCT, it can be difficult, if not impossible, to implement mechanically a multiple-turn helical trajectory on the imaging systems due to hardware constraints. However, imaging systems in these applications often allow for the implementation of a reverse helical trajectory in which the rotation direction changes between two consecutive turns. Because the reverse helical trajectory satisfies Tuy's condition, when projections of the imaged object are nontruncated, it yields data sufficient for exact image reconstruction within the reverse helix volume. The recently developed chord-based algorithms such as the backprojection filtration (BPF) algorithm can readily be applied to reconstructing images on chords of a reverse helical trajectory, and they can thus reconstruct an image within a volume covered by the chords. Conversely, the chord-based algorithms cannot reconstruct images within regions that are not intersected by chords. In a reverse helix volume, as shown below, chordless regions exist in which no images can thus be reconstructed by use of the chord-based algorithms. In this work, based upon Pack-Noo's formula, a shift-invariant filtered backprojection (FBP) algorithm is derived for exact image reconstruction within the reverse helix volume, including the chordless region. Numerical studies have also been conducted to demonstrate the chordless region in a reverse helix volume and to validate the FBP algorithm for image reconstruction within the chordless region. Results of the numerical studies confirm that the FBP algorithm can exactly reconstruct an image within the entire reverse helix volume, including the chordless region. It is relatively straightforward to extend the FBP algorithm to reconstruct images for general trajectories, including reverse helical trajectories with variable pitch, tilted axis, and/or additional segments between turns.     

Angular weighted hybrid cone-beam CT reconstruction for circular trajectories.

Hybrid reconstruction techniques have been introduced for the volume reconstruction of axially truncated cone-beam computed tomography projection data acquired along a circular source-detector trajectory. The introduction of weighted half-scan techniques into this framework is described in this paper. Due to the cone-beam geometry it is not possible to perform the weighting on the projections as is typically done in conventional single-line computed tomography. Hence, in this paper we present an efficient way to incorporate angular weighting functions, depending on the object point position, into the framework of hybrid cone-beam reconstruction. Four different angular weighting functions are introduced and discussed with respect to their cone-beam artefact behaviour and their influence on the signal-to-noise ratio. As a result, the most effective angular weighting function for hybrid circular cone-beam reconstruction is determined by means of a simulation study based on mathematical phantoms and clinical data sets. This distance-weighted angular weighting scheme yields the best results in terms of high image quality, low computational complexity and signal-to-noise variations in the reconstruction volume.     

Convergence of the maximum likelihood reconstruction algorithm for emission computed tomography

Convergence properties of the maximum likelihood estimator (MLE) for emission computed tomographic (ECT) image reconstruction are evaluated as a function of Poisson noise, precision of the assumed system resolution model and iteration number up to 10,000 iterations. In the ECT reconstruction problem, the photon-emitting source distribution is to be estimated from measurements of projections of the emitted photon flux. The MLE algorithm seeks a source distribution which will maximise the maximum likelihood function relating the estimated and the measured projections. A Monte Carlo model of the system transfer function of a single photon emission computed tomographic (SPECT) system allowed realistic projection data to be simulated from a known source distribution. Poisson noise was added to the Monte Carlo simulations. By using projection data from a known source distribution generated through a known system transfer function, we were able to simultaneously evaluate the convergence of both the projection estimations as well as the source distribution estimations. As predicted by theory, the estimates of the projections did continue to improve (or remain the same) for all combinations of Poisson noise (up to 10% RMS) and system resolution (+/- 10% of true value) tested. Convergence of source distribution estimates to the true value was found for up to 10,000 iterations only for low noise (0.1% RMS) with the correct resolution function. For all other combinations, there was some optimum iteration (between 30 and 400) after which the source estimate was degraded even though the estimate of the projections was improved.     

Minimum data image reconstruction algorithms with shift-invariant filtering for helical, cone-beam CT

We derive accurate and efficient reconstruction algorithms for helical, cone-beam CT that employ shift-invariant filtering. Specifically, a new backprojection-filtration algorithm is developed, and a minimum data filtered-backprojection algorithm is derived. These reconstruction algorithms with shift-invariant filtering can accept data with transverse truncation, and hence allow for minimum data image reconstruction.     

Filtered maximum likelihood expectation maximization based global reconstruction for bioluminescence tomography

The reconstruction of bioluminescence tomography (BLT) is severely ill-posed due to the insufficient measurements and diffuses nature of the light propagation. Predefined permissible source region (PSR) combined with regularization terms is one common strategy to reduce such ill-posedness. However, the region of PSR is usually hard to determine and can be easily affected by subjective consciousness. Hence, we theoretically developed a filtered maximum likelihood expectation maximization (fMLEM) method for BLT. Our method can avoid predefining the PSR and provide a robust and accurate result for global reconstruction. In the method, the simplified spherical harmonics approximation (SP_N) was applied to characterize diffuse light propagation in medium, and the statistical estimation-based MLEM algorithm combined with a filter function was used to solve the inverse problem. We systematically demonstrated the performance of our method by the regular geometry- and digital mouse-based simulations and a liver cancer-based in vivo experiment.

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Graphical abstract The filtered MLEM-based global reconstruction method for BLT.