Hybrid reconstruction algorithm for x-ray computed tomography

A hybrid reconstruction algorithm (HRA) is derived for fan beam geometry for use with systems utilizing a linear array of detectors. The algorithm uses fan beam geometry with a modified parallel beam reconstruction formula. The parallel beam algorithm is used with fan beam geometry by a simple geometric conversion and a different back projection formula. Correction for center of rotation shift is done during the back projection. Computer simulations are shown, both with the center of rotation shift uncorrected and corrected.     

Image reconstruction algorithm for single-photon-emission computed tomography with uniform attenuation

A new method is presented for obtaining an analytical solution to the image-reconstruction problem in single-photon-emission computed tomography. The rigorous solution is introduced by applying an analytical continuation process to the two-dimensional Fourier transform of the image, which is derived from the one-dimensional Fourier transforms of projection functions. The calculations can be carried out in a short computation time without involving unstable procedures. Numerical simulations were made to demonstrate the effectiveness of the proposed method.     

Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation

This paper describes a statistical image reconstruction method for x-ray CT that is based on a physical model that accounts for the polyenergetic x-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. Unlike our earlier work, the proposed algorithm does not require pre-segmentation of the object into the various tissue classes (e.g., bone and soft tissue) and allows mixed pixels. The attenuation coefficient of each voxel is modelled as the product of its unknown density and a weighted sum of energy-dependent mass attenuation coefficients. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown density of each voxel. Applying this method to simulated x-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artefacts relative to conventional beam hardening correction methods. We also apply the method to real data acquired from a phantom containing various concentrations of potassium phosphate solution. The algorithm reconstructs an image with accurate density values for the different concentrations, demonstrating its potential for quantitative CT applications.     

Convolutional image reconstruction for quantitative single photon emission computed tomography

Two image reconstruction algorithms have been investigated. They are based on filtered backprojection, and are useful when the tissue attenuation is considered to be uniform in the object. The first method uses a weighted backprojection, the weighting factor being determined in such a way that the photon attenuation is compensated with low noise propagation. The parameters involved in the convolution kernel and the correction function were determined by a computer iteration program. The second method, which is a simplified version of the first, uses conventional backprojection, and takes a shorter computation time than the first method. The statistical noise of an image can be minimised by suitable positioning of the coordinate origin for the reconstruction. The theory of the two methods, their performance on statistical noise and some results of mathematical and experimental phantom studies are described.     

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.     

PI-line-based image reconstruction in helical cone-beam computed tomography with a variable pitch

Current applications of helical cone-beam computed tomography (CT) involve primarily a constant pitch where the translating speed of the table and the rotation speed of the source-detector remain constant. However, situations do exist where it may be more desirable to use a helical scan with a variable translating speed of the table, leading a variable pitch. One of such applications could arise in helical cone-beam CT fluoroscopy for the determination of vascular structures through real-time imaging of contrast bolus arrival. Most of the existing reconstruction algorithms have been developed only for helical cone-beam CT with constant pitch, including the backprojection-filtration (BPF) and filtered-backprojection (FBP) algorithms that we proposed previously. It is possible to generalize some of these algorithms to reconstruct images exactly for helical cone-beam CT with a variable pitch. In this work, we generalize our BPF and FBP algorithms to reconstruct images directly from data acquired in helical cone-beam CT with a variable pitch. We have also performed a preliminary numerical study to demonstrate and verify the generalization of the two algorithms. The results of the study confirm that our generalized BPF and FBP algorithms can yield exact reconstruction in helical cone-beam CT with a variable pitch. It should be pointed out that our generalized BPF algorithm is the only algorithm that is capable of reconstructing exactly region-of-interest image from data containing transverse truncations.     

A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter form factor of the investigated object. Reconstruction from coherently scattered x-rays is commonly done using algebraic reconstruction techniques (ART). In this paper, we propose an alternative approach based on filtered back-projection. For the first time, a three-dimensional (3D) filtered back-projection technique using curved 3D back-projection lines is applied to two-dimensional coherent scatter projection data. The proposed algorithm is tested with simulated projection data as well as with projection data acquired with a demonstrator setup similar to a multi-line CT scanner geometry. While yielding comparable image quality as ART reconstruction, the modified 3D filtered back-projection algorithm is about two orders of magnitude faster. In contrast to iterative reconstruction schemes, it has the advantage that subfield-of-view reconstruction becomes feasible. This allows a selective reconstruction of the coherent-scatter form factor for a region of interest. The proposed modified 3D filtered back-projection algorithm is a powerful reconstruction technique to be implemented in a CSCT scanning system. This method gives coherent scatter CT the potential of becoming a competitive modality for medical imaging or nondestructive testing.     

Optimal noise control in and fast reconstruction of fan-beam computed tomography image.

We proposed a linear approach that exploits statistically complementary information inherent in the projection data of fan-beam computed tomography (CT) for achieving a bias-free image-variance reduction in fan-beam CT. This linear approach leads to the development of infinite classes of hybrid algorithms for image reconstruction in fan-beam CT. These hybrid algorithms are computationally more efficient and numerically less susceptible to data noise and to the effect of finite sampling than the conventional fan-beam filtered back-projection (FFBP) algorithm. We also developed infinite classes of generalized fan-beam filtered back-projection (GFFBP) algorithms, which include the conventional FFBP algorithm as a special member. We demonstrated theoretically and quantitatively that the hybrid and GFFBP algorithms are identical (or different) in the absence (or presence) of data noise and of the effect of finite sampling. More importantly, we identified the statistically optimal hybrid algorithm that may have potentially significant implication to image reconstruction in fan-beam CT. Extensive numerical results of computer-simulation studies validated our theoretical results.     

Prospects for quantitative computed tomography imaging in the presence of foreign metal bodies using statistical image reconstruction

X-ray computed tomography (CT) images of patients bearing metal intracavitary applicators or other metal foreign objects exhibit severe artifacts including streaks and aliasing. We have systematically evaluated via computer simulations the impact of scattered radiation, the polyenergetic spectrum, and measurement noise on the performance of three reconstruction algorithms: conventional filtered backprojection (FBP), deterministic iterative deblurring, and a new iterative algorithm, alternating minimization (AM), based on a CT detector model that includes noise, scatter, and polyenergetic spectra. Contrary to the dominant view of the literature, FBP streaking artifacts are due mostly to mismatches between FBP's simplified model of CT detector response and the physical process of signal acquisition. Artifacts on AM images are significantly mitigated as this algorithm substantially reduces detector-model mismatches. However, metal artifacts are reduced to acceptable levels only when prior knowledge of the metal object in the patient, including its pose, shape, and attenuation map, are used to constrain AM's iterations. AM image reconstruction, in combination with object-constrained CT to estimate the pose of metal objects in the patient, is a promising approach for effectively mitigating metal artifacts and making quantitative estimation of tissue attenuation coefficients a clinical possibility.     

成人寰枢正中关节间隙正常值的CT多平面重组测量

目的 测量MSCT影像成人寰枢正中关节间隙(MADI)的正常值范围,探讨MADI值与年龄和性别的关系。方法 选取2009年8月—2014年7月山东省医学影像研究所18岁以上行寰齿关节MSCT扫描的700例患者影像资料行回顾性分析,排除外伤、累及上颈椎各类疾病者,按年龄分为18～24岁、25～29岁、30～39 岁、40～49岁、50～59 岁、60～69 岁 和≥70 岁7组,每组入选100例。对寰齿关节正中矢状位CT影像进行多平面重组,并测量寰椎前后结节中点连线经过寰齿关节间隙的长度,即MADI。计算不同年龄组患者MADI值,并采用线性回归方法进一步分析MADI值与年龄、性别的关系。 结果 7组由低至高不同年龄患者的MADI值依次为(1.77±0.39)mm、(1.61±0.37)mm、(1.58±0.36)mm、(1.41±0.29) mm、(1.34±0.28)mm 、(1.31±0.29)mm、和(1.06±0.47)mm,MADI 随年龄增加而递减 (r=-0.511, P＜0.01)。男性MADI(1.50±0.36)mm,女性MADI(1.38±0.34)mm,MADI 在不同性别之间无相关性 (r=0.000, P＞0.05)。结论 在MSCT正中矢状位上MADI值与年龄呈负相关,与性别无关。     

An error-reduction-based algorithm for cone-beam computed tomography

Image reconstruction from cone-beam projections collected along a single circular source trajectory is commonly done using the Feldkamp algorithm, which performs well only with a small cone angle. In this report, we propose an error-reduction-based algorithm to increase the cone angle by several folds to achieve satisfactory image quality at the same radiation dose. In our scheme, we first reconstruct the object using the Feldkamp algorithm. Then, we synthesize cone-beam projection data from the reconstructed volume in the same geometry, and reconstruct the volume again from the synthesized projections. Finally, these two reconstruction results are combined to reduce the reconstruction error and produce a superior image volume. The merit of this algorithm is demonstrated in numerical simulation.     

Iterative concurrent reconstruction algorithms for emission computed tomography

Direct reconstruction techniques, such as those based on filtered backprojection, are typically used for emission computed tomography (ECT), even though it has been argued that iterative reconstruction methods may produce better clinical images. The major disadvantage of iterative reconstruction algorithms, and a significant reason for their lack of clinical acceptance, is their computational burden. We outline a new class of 'concurrent' iterative reconstruction techniques for ECT in which the reconstruction process is reorganized such that a significant fraction of the computational processing occurs concurrently with the acquisition of ECT projection data. These new algorithms use the 10-30 min required for acquisition of a typical SPECT scan to iteratively process the available projection data, significantly reducing the requirements for post-acquisition processing. These algorithms are tested on SPECT projection data from a Hoffman brain phantom acquired with a 2 x 10(5) counts in 64 views each having 64 projections. The SPECT images are reconstructed as 64 x 64 tomograms, starting with six angular views. Other angular views are added to the reconstruction process sequentially, in a manner that reflects their availability for a typical acquisition protocol. The results suggest that if T s of concurrent processing are used, the reconstruction processing time required after completion of the data acquisition can be reduced by at least 1/3T s.     

Iterative reconstruction techniques in emission computed tomography

In emission tomography statistically based iterative methods can improve image quality relative to analytic image reconstruction through more accurate physical and statistical modelling of high-energy photon production and detection processes. Continued exponential improvements in computing power, coupled with the development of fast algorithms, have made routine use of iterative techniques practical, resulting in their increasing popularity in both clinical and research environments. Here we review recent progress in developing statistically based iterative techniques for emission computed tomography. We describe the different formulations of the emission image reconstruction problem and their properties. We then describe the numerical algorithms that are used for optimizing these functions and illustrate their behaviour using small scale simulations.     

Predicting calyceal access for percutaneous nephrolithotomy with computed tomography multiplanar reconstruction

OBJECTIVES:

Objective parameters in computed tomography (CT) scans that could predict calyceal access during percutaneous nephrolithotomy have not been evaluated. These parameters could improve access planning for percutaneous nephrolithotomy. We aimed to determine which parameters extracted from a preoperative multiplanar reconstructed CT could predict renal calyceal access during a percutaneous nephrolithotomy.

METHODS:

From January 2009 through April 2011, 230 patients underwent 284 percutaneous nephrolithotomies at our institution. Sixteen patients presented with complete staghorn calculi, and 11 patients (13 renal units) were analyzed. Five parameters were extracted from a preoperative reconstructed CT and compared with the surgical results of percutaneous nephrolithotomy.

RESULTS:

Fifty-eight calyces were studied, with an average of 4.4 calyces per procedure. A rigid nephroscope was used to access a particular calyx, and a univariate analysis showed that the entrance calyx had a smaller length (2.7 vs. 3.98 cm, p = 0.018). The particular calyx to be accessed should have a smaller length (2.22 vs. 3.19 cm, p = 0.012), larger angles (117.6 vs. 67.96, p<0.001) and larger infundibula (0.86 vs. 0.61 cm, p = 0.002). In the multivariate analysis, the only independent predictive factor for accessing a particular calyx was the angle between the entrance calyx and the calyx to be reached (OR 1.15, 95% confidence interval [CI], 1.053–1.256, p = 0.002).

CONCLUSION:

The angle between calyces obtained by multiplanar CT reconstruction is the only predictor of calyx access.     

Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography

Among the iterative reconstruction algorithms for tomography, the multiplicative algebraic reconstruction technique (MART) has two advantages that make it stand out from other algorithms: it confines the image (and therefore the projection data) to the convex hull of the patient, and it maximizes entropy. In this paper, we have undertaken a series of experiments to determine the importance of MART nonlinearity to image quality. Variants of MART were implemented aiming to exploit and exaggerate the nonlinear properties of the algorithm. We introduce the Power MART, Boxcar Averaging MART and Bouncing MART algorithms. Power MART is linked to the relaxation concept. Its behaviour is similar to that of the chaos of a logistic equation. There appears to be an antagonism between increasing nonlinearity and noise in the projection data. The experiments confirm our general observation that regularization as a means of solving simultaneous linear equations that are underdetermined is suboptimal: it does not necessarily select the correct image from the hyperplane of solutions, and so does not maximize the image quality:x-ray dose ratio. Our investigations prove that there is scope to optimize CT algorithms and thereby achieve greater dose reduction.     

Kymogram detection and kymogram-correlated image reconstruction from subsecond spiral computed tomography scans of the heart

Subsecond single-slice, multi-slice or cone-beam spiral computed tomography (SSCT, MSCT, CBCT) offer great potential for improving heart imaging. Together with the newly developed phase-correlated cardiac reconstruction algorithms 180 degrees MCD and 180 degrees MCI [Med. Phys. 27, 1881-1902 (2000)] or related algorithms provided by the CT manufacturers, high image quality can be achieved. These algorithms require information about the cardiac motion, i.e., typically the simultaneously recorded electrocardiogram (ECG), to synchronize the reconstruction with the cardiac motion. Neither data acquired without ECG information (standard patients) nor acquisitions with corrupted ECG information can be handled adequately. We developed a method to extract the appropriate information about cardiac motion directly from the measured raw data (projection data). The so-called kymogram function is a measure of the cardiac motion as a function of time t or as a function of the projection angle alpha. In contrast to the ECG which is a global measure of the heart's electric excitation, the kymogram is a local measure of the heart motion at the z-position z(a) at projection angle a. The patient's local heart rate as well as the necessary synchronization information to be used with phase-correlated algorithms can be extracted from the kymogram by using a series of signal processing steps. The kymogram information is shown to be adequate to substitute the ECG information. Computer simulations with simulated ECG and patient measurements with simultaneously acquired ECG were carried out for a multislice scanner providing M = 4 slices to evaluate these new approaches. Both the ECG function and the kymogram function were used for reconstruction. Both were highly correlated regarding the periodicity information used for reconstruction. In 21 out of 25 consecutive cases the kymogram approach was equivalent to the ECG-correlated reconstruction; only minor differences in image quality between both methods were observed. For one patient the synchronization information detected by the ECG monitor turned out to be wrong; here, the kymogram constituted the only approach that provided useful reconstructions. Patient studies with 12 and 16 slices indicate the usefulness of our approach for cone-beam CT scans. Kymogram-correlated reconstructions also appear to have the potential to improve imaging of pericardial lung areas in general.     

Fast reconstruction with uniform noise properties in halfscan computed tomography

The hybrid algorithms developed recently for the reconstruction of fan-beam images possess computational and noise properties superior to those of the fan-beam filtered backprojection (FFBP) algorithm. However, the hybrid algorithms cannot be applied directly to a halfscan fan-beam sinogram because they require knowledge of a fullscan fan-beam sinogram. In this work, we developed halfscan-hybrid algorithms for image reconstruction in halfscan computed tomography (CT). Numerical evaluation indicates that the proposed halfscan-hybrid algorithms are computationally more efficient than are the widely used halfscan-FFBP algorithms. Also, the results of quantitative studies demonstrated clearly that the noise levels in images reconstructed by use of the halfscan-hybrid algorithm are generally lower and spatially more uniform than are those in images reconstructed by use of the halfscan-FFBP algorithm. Such reduced and uniform image noise levels may be translated into improvement of the accuracy and precision of lesion detection and parameter estimation in noisy CT images without increasing the radiation dose to the patient. Therefore, the halfscan-hybrid algorithms may have significant implication for image reconstruction in conventional and helical CT.     

A local region of interest image reconstruction via filtered backprojection for fan-beam differential phase-contrast computed tomography

Recently, x-ray differential phase contrast computed tomography (DPC-CT) has been experimentally implemented using a conventional source combined with several gratings. Images were reconstructed using a parallel-beam reconstruction formula. However, parallel-beam reconstruction formulae are not directly applicable for a large image object where the parallel-beam approximation fails. In this note, we present a new image reconstruction formula for fan-beam DPC-CT. There are two major features in this algorithm: (1) it enables the reconstruction of a local region of interest (ROI) using data acquired from an angular interval shorter than 180 degrees + fan angle and (2) it still preserves the filtered backprojection structure. Numerical simulations have been conducted to validate the image reconstruction algorithm.