可变约束OS-EM图像重建算法仿真研究

有序子集最大期望值方法 (OrderedSubsetsExpectationMaximization ,OS EM )具有较高的重建图像质量和较短的计算时间 ,正逐步应用在正电子发射断层成像仪 (PositionEmissionTomography ,PET)图像重建过程中。本研究提出了一种改进的OS EM图像重建算法可变约束OS EM迭代算法 (VariableConstraintOS EM ,VCOSEM) ,对仿真Phantom模型在不同测量条件以及不同子集划分情况下的研究结果表明 ,该方法具有分辨率高 ,噪声低的优点 ,能够提高重建图像质量。     

A fast image reconstruction algorithm based on penalized-likelihood estimate

Statistical iterative methods for image reconstruction like maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurately modeling the counting statistics and the photon transport during acquisition. They are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to the conventional filtered back projection algorithm. But a major drawback of the statistical iterative image reconstruction is its high computational cost. In this paper, a fast algorithm is proposed as a modified OS-EM (MOS-EM) using a penalized function, which is applied to the least squares merit function to accelerate image reconstruction and to achieve better convergence. The experimental results show that the algorithm can provide high quality reconstructed images with a small number of iterations.     

Simultaneous iterative reconstruction of emission and attenuation images in positron emission tomography from emission data only

For quantitative image reconstruction in positron emission tomography attenuation correction is mandatory. In case that no data are available for the calculation of the attenuation correction factors one can try to determine them from the emission data alone. However, it is not clear if the information content is sufficient to yield an adequate attenuation correction together with a satisfactory activity distribution. Therefore, we determined the log likelihood distribution for a thorax phantom depending on the choice of attenuation and activity pixel values to measure the crosstalk between both. In addition an iterative image reconstruction (one-dimensional Newton-type algorithm with a maximum likelihood estimator), which simultaneously reconstructs the images of the activity distribution and the attenuation coefficients is used to demonstrate the problems and possibilities of such a reconstruction. As result we show that for a change of the log likelihood in the range of statistical noise, the associated change in the activity value of a structure is between 6% and 263%. In addition, we show that it is not possible to choose the best maximum on the basis of the log likelihood when a regularization is used, because the coupling between different structures mediated by the (smoothing) regularization prevents an adequate solution due to crosstalk. We conclude that taking into account the attenuation information in the emission data improves the performance of image reconstruction with respect to the bias of the activities, however, the reconstruction still is not quantitative.     

Local and Non-local Regularization Techniques in Emission (PET/SPECT) Tomographic Image Reconstruction Methods

Emission tomographic image reconstruction is an ill-posed problem due to limited and noisy data and various image-degrading effects affecting the data and leads to noisy reconstructions. Explicit regularization, through iterative reconstruction methods, is considered better to compensate for reconstruction-based noise. Local smoothing and edge-preserving regularization methods can reduce reconstruction-based noise. However, these methods produce overly smoothed images or blocky artefacts in the final image because they can only exploit local image properties. Recently, non-local regularization techniques have been introduced, to overcome these problems, by incorporating geometrical global continuity and connectivity present in the objective image. These techniques can overcome drawbacks of local regularization methods; however, they also have certain limitations, such as choice of the regularization function, neighbourhood size or calibration of several empirical parameters involved. This work compares different local and non-local regularization techniques used in emission tomographic imaging in general and emission computed tomography in specific for improved quality of the resultant images.     

An improved ordered subsets expectation maximization positron emission computerized tomography reconstruction

Ordered subsets expectation maximization (OS-EM) reconstruction method is usually used in positron emission tomography (PET). But it has some disadvantage such as long computation time and bad reconstruction quality. Filtered back projection (FBP), that has many advantages such as simple structure and short reconstruction time, is firstly introduced into the initialization stage of the OS-EM to fast the reconstruction process. Then, the smoothness method is applied after the OS-EM algorithm to improve the reconstruction speed and quality. The reconstructed images are compared for both the simulated phantom data and the brain magnetic resonance imaging data. The improved OS-EM is shown to be more feasible than the standard OS-EM within the same iteration steps and in higher signal noise ratio (SNR) condition.     

An iterative transmission algorithm incorporating cross-talk correction for SPECT

Simultaneous emission/transmission acquisitions in cardiac SPECT with a Tc99m/Gd153 source combination offer the capability for nonuniform attenuation correction. However, cross-talk of Tc99m photons downscattered into the Gd153 energy window contaminates the reconstructed transmission map used for attenuation correction. The estimated cross-talk contribution can be subtracted prior to transmission reconstruction or incorporated in the reconstruction algorithm itself. In this work, we propose an iterative transmission algorithm (MLTG-S) based on the maximum-likelihood gradient algorithm (MLTG) that explicitly accounts for this cross-talk estimate. Clinical images were acquired on a three-headed SPECT camera, acquiring Tc99m emission and Gd153 transmission images simultaneously. Subtracting the cross-talk estimate prior to transmission reconstruction can result in negative and zero values if the estimate is larger than or equal to the count in the transmission projection bin, especially with increased attenuator size or amount of cross-talk. This results in inaccurate attenuation coefficients for MLTG reconstructions with cross-talk subtraction. MLTG-S reconstructions on the other hand, yield better estimates of attenuation maps, by avoiding the subtraction of the cross-talk estimate. Comparison of emission slices corrected for nonuniform attenuation reveals that inaccuracies in the reconstructed attenuation map caused by cross-talk can artificially enhance the extra-cardiac activity, confounding the ability to visualize the left-ventricular walls.     

Accelerated EM reconstruction in total-body PET: potential for improving tumour detectability

Total-body positron emission tomography (PET) is a useful diagnostic tool for evaluating malignant disease. However, tumour detection is limited by image artefacts due to the lack of attenuation correction and noise. Attenuation correction may be possible using transmission data acquired after or simultaneously with emission data. Despite the elimination of attenuation artefacts, however, tumour detection is still hampered by noise, which is amplified during image reconstruction by filtered backprojection (FBP). We have investigated, as an alternative to FBP, an accelerated expectation maximization (EM) algorithm for its potential to improve tumour detectability in total-body PET. Signal to noise ratio (SNR), calculated for a tumour with respect to the surrounding background, is used as a figure of merit. A software tumour phantom, with conditions typical of those encountered in a total-body PET study using simultaneous acquisition, is used to optimize and compare various reconstruction approaches. Accelerated EM reconstruction followed by two-dimensional filtering is shown to yield significantly higher SNR than FBP for a range of tumour sizes, concentrations and counting statistics (deltaSNR = 6.3 +/- 3.9, p < 0.001). The methods developed are illustrated by examples derived from physical phantom and patient data.     

Subsets and overrelaxation in iterative image reconstruction.

A number of iterative image reconstruction algorithms were integrated into one formula characterizing each algorithm by only two parameters: overrelaxation and number of subsets. From the formula it follows that the ordered-subsets iteration (OS-EM) is equivalent to iteration with overrelaxation, where the OS level corresponds to the overrelaxation parameter. Algorithms represented by the formula were studied with respect to speed of convergence and image characteristics. In particular, OS-EM was compared with a single-projection iteration procedure using an optimized sequence of overrelaxation parameters (HOSP) which combines rapid convergence with reduced storage requirements. As a result, OS-EM with a constant number of subsets either needed more iteration steps than HOSP or provoked additional noise, depending on the number of subsets used during iteration. OS-EM can be improved by using decreasing OS levels, imitating the decreasing overrelaxation parameters used for HOSP. The resulting OS-EM may be slightly more rapid than HOSP, due to the increasing number of projections used simultaneously.     

Accurate attenuation correction for a 3D PET system

An accurate attenuation correction has been developed for a small-volume three-dimensional positron emission tomography (PET) system. Transmission data were measured as twenty-four 2D slices which were reconstructed and combined to form a 3D attenuation image. Emission data were reconstructed using a backproject-then-filter technique, and each event was corrected for attenuation at backprojection time by a reprojection through the attenuation image. This correction restores the spatial invariance of the point response function, thus allowing a valid deconvolution and producing an undistorted emission image. Scattering corrections were not applied to either the transmission or the emission data but simulation studies indicated that scattering made only a small contribution to the attenuation measurement. Results are presented for two phantoms, in which transmission scans of 57,500 and 18,700 events/slice were used to correct emission images of 5.2 and 2.8 million events. Although the attenuation images had poor statistical accuracy and a resolution of 13 mm, the method resulted in accurate attenuation-corrected images with no degradation in image resolution (which was 3 mm for the first emission image), and with little effect on image noise.     

Novel approach to stationary transmission scanning using Compton scattered radiation

Transmission scanning-based estimation of the attenuation map plays a crucial role in quantitative radionuclide imaging. X-ray computed tomography (CT) reconstructs directly the attenuation coefficients map from data transmitted through the object. This paper proposes an alternative route for reconstructing the object attenuation map by exploiting Compton scatter of transmitted radiation from an externally placed radionuclide source. In contrast to conventional procedures, data acquisition is realized as a series of images parameterized by the Compton scattering angle and registered on a stationary gamma camera operating without spatial displacement. Numerical simulation results using realistic voxel-based phantoms are presented to illustrate the efficiency of this new transmission scanning approach for attenuation map reconstruction. The encouraging results presented in this paper may suggest the possibility of proposing a new concept for emission/transmission imaging using scattered radiation, which has many advantages compared to conventional technologies.     

Simultaneous iterative reconstruction for emission and attenuation images in positron emission tomography

The quality of the attenuation correction strongly influences the outcome of the reconstructed emission scan in positron emission tomography. Usually the attenuation correction factors are calculated from the transmission and blank scan and thereafter applied during the reconstruction on the emission data. However, this is not an optimal treatment of the available data, because the emission data themselves contain additional information about attenuation: The optimal treatment must use this information for the determination of the attenuation correction factors. Therefore, our purpose is to investigate a simultaneous emission and attenuation image reconstruction using a maximum likelihood estimator, which takes the attenuation information in the emission data into account. The total maximum likelihood function for emission and transmission is used to derive a one-dimensional Newton-like algorithm for the calculation of the emission and attenuation image. Log-likelihood convergence, mean differences, and the mean of squared differences for the emission image and the attenuation correction factors of a mathematical thorax phantom were determined and compared. As a result we obtain images improved with respect to log likelihood in all cases and with respect to our figures of merit in most cases. We conclude that the simultaneous reconstruction can improve the performance of image reconstruction.     

Quantitative pulmonary single photon emission computed tomography for radiotherapy applications.

Pulmonary imaging using single photon emission computed tomography (SPECT) is the focus of current radiotherapy research, including dose-response analysis and three-dimensional (3D) radiation treatment planning. Improvement in the quantitative capability of SPECT may help establish its potential role in this application as well as others requiring accurate knowledge of pulmonary blood flow. The purposes of this study were to quantitatively evaluate SPECT filtered backprojection (FBP) and ordered subset-expectation maximization (OS-EM) reconstruction implementations for measuring absolute activity concentration in lung phantom experiments, and to incorporate quantitative SPECT techniques in 3D-RTP for lung cancer. Quantitative FBP (nonuniform iterative Chang attenuation compensation, scatter correction, and 3D postreconstruction Metz filtering) and OS-EM implementations were compared with a "clinical" implementation of FBP (uniform multiplicative Chang attenuation compensation and post-reconstruction von Hann filtering), for their ability to improve quantification of inactive and active spherical defects in the lungs of an anthropomorphic torso phantom. Activity concentration estimates were found to depend on many factors, such as region of interest size, scatter subtraction constant (k), postreconstruction deconvolution filtering and, in the case of OS-EM, total number of iterations. In general, reconstruction implementations incorporating compensation for nonuniform attenuation and scatter provided reduced bias relative to the clinical implementation. Potential applications to lung radiotherapy, including dose-functional histograms and treatment planning are also discussed. SPECT has the potential to provide accurate estimates of lung activity distributions that, together with improved image quality, may be useful for the study and prediction of therapeutic response.     

Fundamental study on diffuse reflective optical tomography

We report a simulation study on diffuse reflective optical computed tomography, in which continuous-wave sources and detectors are placed on the plane surface of a semi-infinite body. We adopted a simple Tikhonov regularization in the inverse problem and demonstrated the feasibility of three-dimensional reconstruction of the absorption coefficient change. The spatial resolution of the reconstructed image was shown to be degrading markedly with the depth. The regularization parameter should be chosen appropriately considering the trade-off between the reconstructed image noise and the spatial resolution. We analysed the dependence of the spatial resolution of the reconstructed image on the regularization parameter and the depth, and also the behaviour of the reconstructed image noise on the regularization parameter and the depth.     

Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty

Iterative algorithms such as maximum likelihood-expectation maximization (ML-EM) become the standard for the reconstruction in emission computed tomography. However, such algorithms are sensitive to noise artifacts so that the reconstruction begins to degrade when the number of iterations reaches a certain value. In this paper, we have investigated a new iterative algorithm for penalized-likelihood image reconstruction that uses the fuzzy nonlinear anisotropic diffusion (AD) as a penalty function. The proposed algorithm does not suffer from the same problem as that of ML-EM algorithm, and it converges to a low noisy solution even if the iteration number is high. The fuzzy reasoning instead of a nonnegative monotonically decreasing function was used to calculate the diffusion coefficients which control the whole diffusion. Thus, the diffusion strength is controlled by fuzzy rules expressed in a linguistic form. The proposed method makes use of the advantages of fuzzy set theory in dealing with uncertain problems and nonlinear AD techniques in removing the noise as well as preserving the edges. Quantitative analysis shows that the proposed reconstruction algorithm is suitable to produce better reconstructed images when compared with ML-EM, ordered subsets EM (OS-EM), Gaussian-MAP, MRP, TV-EM reconstructed images.     

An adaptive Tikhonov regularization method for fluorescence molecular tomography

The high degree of absorption and scattering of photons propagating through biological tissues makes fluorescence molecular tomography (FMT) reconstruction a severe ill-posed problem and the reconstructed result is susceptible to noise in the measurements. To obtain a reasonable solution, Tikhonov regularization (TR) is generally employed to solve the inverse problem of FMT. However, with a fixed regularization parameter, the Tikhonov solutions suffer from low resolution. In this work, an adaptive Tikhonov regularization (ATR) method is presented. Considering that large regularization parameters can smoothen the solution with low spatial resolution, while small regularization parameters can sharpen the solution with high level of noise, the ATR method adaptively updates the spatially varying regularization parameters during the iteration process and uses them to penalize the solutions. The ATR method can adequately sharpen the feasible region with fluorescent probes and smoothen the region without fluorescent probes resorting to no complementary priori information. Phantom experiments are performed to verify the feasibility of the proposed method. The results demonstrate that the proposed method can improve the spatial resolution and reduce the noise of FMT reconstruction at the same time.     

Regularized iterative weighted filtered backprojection for helical cone-beam CT

Contemporary reconstruction methods employed for clinical helical cone-beam computed tomography (CT) are analytical (noniterative) but mathematically nonexact, i.e., the reconstructed image contains so called cone-beam artifacts, especially for higher cone angles. Besides cone artifacts, these methods also suffer from windmill artifacts: alternating dark and bright regions creating spiral-like patterns occurring in the vicinity of high z-direction derivatives. In this article, the authors examine the possibility to suppress cone and windmill artifacts by means of iterative application of nonexact three-dimensional filtered backprojection, where the analytical part of the reconstruction brings about accelerated convergence. Specifically, they base their investigations on the weighted filtered backprojection method [Stierstorfer et al., Phys. Med. Biol. 49, 2209-2218 (2004)]. Enhancement of high frequencies and amplification of noise is a common but unwanted side effect in many acceleration attempts. They have employed linear regularization to avoid these effects and to improve the convergence properties of the iterative scheme. Artifacts and noise, as well as spatial resolution in terms of modulation transfer functions and slice sensitivity profiles have been measured. The results show that for cone angles up to +/-2.78 degrees, cone artifacts are suppressed and windmill artifacts are alleviated within three iterations. Furthermore, regularization parameters controlling spatial resolution can be tuned so that image quality in terms of spatial resolution and noise is preserved. Simulations with higher number of iterations and long objects (exceeding the measured region) verify that the size of the reconstructible region is not reduced, and that the regularization greatly improves the convergence properties of the iterative scheme. Taking these results into account, and the possibilities to extend the proposed method with more accurate modeling of the acquisition process, the authors believe that iterative improvement with non-exact methods is a promising technique for medical CT applications.     

Fuzzy clustering-based segmented attenuation correction in whole-body PET imaging

Segmented attenuation correction is now a widely accepted technique to reduce noise propagation from transmission scanning in positron emission tomography (PET). In this paper, we present a new method for segmenting transmission images in whole-body scanning. This reduces the noise in the correction maps while still correcting for differing attenuation coefficients of specific tissues. Based on the fuzzy C-means (FCM) algorithm, the method segments the PET transmission images into a given number of clusters to extract specific areas of differing attenuation such as air, the lungs and soft tissue, preceded by a median filtering procedure. The reconstructed transmission image voxels are, therefore, segmented into populations of uniform attenuation based on knowledge of the human anatomy. The clustering procedure starts with an overspecified number of clusters followed by a merging process to group clusters with similar properties (redundant clusters) and removal of some undesired substructures using anatomical knowledge. The method is unsupervised, adaptive and allows the classification of both pre- or post-injection transmission images obtained using either coincident 68Ge or single-photon 137Cs sources into main tissue components in terms of attenuation coefficients. A high-quality transmission image of the scanner bed is obtained from a high statistics scan and added to the transmission image. The segmented transmission images are then forward projected to generate attenuation correction factors to be used for the reconstruction of the corresponding emission scan. The technique has been tested on a chest phantom simulating the lungs, heart cavity and the spine, the Rando-Alderson phantom, and whole-body clinical PET studies showing a remarkable improvement in image quality, a clear reduction of noise propagation from transmission into emission data allowing for reduction of transmission scan duration. There was very good correlation (R2 = 0.96) between maximum standardized uptake values (SUVs) in lung nodules measured on images reconstructed with measured and segmented attenuation correction with a statistically significant decrease in SUV (17.03% +/- 8.4%, P < 0.01) on the latter images, whereas no proof of statistically significant differences on the average SUVs was observed. Finally, the potential of the FCM algorithm as a segmentation method and its limitations as well as other prospective applications of the technique are discussed.     

Implementation of a Tc-99m and Ce-139 scanning line source for attenuation correction in SPECT using a dual opposing detector scintillation camera

Image degradation during single photon emission computed tomography (SPECT) due to attenuation and Compton scatter of photons can cause clinical image artifacts and will also result in inaccurate quantitative data. Therefore attenuation correction methods recently received wide interest. Transmission imaging can be performed to obtain the attenuation coefficients of a nonhomogeneous attenuating medium accurately. The aim of this study was firstly to evaluate the imaging characteristics of the scanning line source assembly. The results obtained with Tc-99m and Ce-139 were compared. Secondly the calculated attenuation coefficients were compared with known values from literature, using Tc-99m and Ce-139 as transmission sources. Lastly the method of acquiring simultaneous transmission and emission data was investigated. This study shows that an attenuation coefficient map can be obtained using a scanning line source for transmission imaging with a dual opposing detector camera. The imaging characteristics of Tc-99m and Ce-139 as transmission sources are similar. The resolution obtained with the Ce-139 line source was poorer than that obtained with the Tc-99m line source. A linear relationship was found between CT numbers and attenuation coefficients for transmission images using both Tc-99m and Ce-139 line sources. The attenuation coefficient value for water was underestimated by 1% using the Tc-99m transmission source and underestimated by 10% using Ce-139 as transmission source. This underestimation of attenuation coefficient values was also obtained in the human study. A myocardial perfusion study processed without and with attenuation correction clearly demonstrated the effect of the attenuation correction in the inferior myocardial region. The potential of using a scanning line source as transmission source with a dual opposing detector camera has been demonstrated in this study. The transmission source, Ce-139 was successfully introduced in this investigation for simultaneous acquisition of transmission and emission data.     

Differential attenuation method for simultaneous estimation of activity and attenuation in multiemission single photon emission computed tomography

A penalized weighted least squares reconstruction algorithm is described that simultaneously estimates activity and attenuation distributions from emission sinogram data alone. This estimation technique is based on differential attenuation information and is applicable to any single photon emission computed tomography imaging isotope with emissions at two or more distinct energies, after accurate compensation for Compton scatter. A rotation-based forward projector is used to efficiently model photon attenuation at multiple emission energies, as well as distance-dependent spatial resolution. The algorithm was tested using simulated scatter-free 201T1 projection data from a single-slice numerical cardiac phantom with and without cold myocardial defects. Poisson noise was added to the projection data to mimic clinically realistic count densities. The activity estimates resulting from the proposed method had fewer artifacts and were substantially more accurate than images reconstructed with filtered backprojection without compensation for attenuation. Several techniques were employed to reduce the time required for the iterative routine to converge and to reduce the sensitivity of the solution to noise in the projection data. These included: (1) a preconditioning image variable transformation; (2) a coarse-to-fine grid initialization schedule; and (3) a convex hull image mask determined directly from the data. The combined effect of these techniques substantially reduced the compute time required for the reconstruction.     

Accelerated median root prior reconstruction for pinhole single-photon emission tomography (SPET)

Pinhole collimation can be used to improve spatial resolution in SPET. However, the resolution improvement is achieved at the cost of reduced sensitivity, which leads to projection images with poor statistics. Images reconstructed from these projections using the maximum likelihood expectation maximization (ML-EM) algorithms, which have been used to reduce the artefacts generated by the filtered backprojection (FBP) based reconstruction, suffer from noise/bias trade-off: noise contaminates the images at high iteration numbers, whereas early abortion of the algorithm produces images that are excessively smooth and biased towards the initial estimate of the algorithm. To limit the noise accumulation we propose the use of the pinhole median root prior (PH-MRP) reconstruction algorithm. MRP is a Bayesian reconstruction method that has already been used in PET imaging and shown to possess good noise reduction and edge preservation properties. In this study the PH-MRP algorithm was accelerated with the ordered subsets (OS) procedure and compared to the FBP, OS-EM and conventional Bayesian reconstruction methods in terms of noise reduction, quantitative accuracy, edge preservation and visual quality. The results showed that the accelerated PH-MRP algorithm was very robust. It provided visually pleasing images with lower noise level than the FBP or OS-EM and with smaller bias and sharper edges than the conventional Bayesian methods.