[en] Transmission scans are necessary for estimating the attenuation correction factors (ACFs) to yield quantitatively accurate PET emission images. To reduce the total scan time, post-injection transmission scans have been proposed in which one can simultaneously acquire emission and transmission data using rod sources and sinogram windowing. However, since the post-injection transmission scans are corrupted by emission coincidences, accurate correction for attenuation becomes more challenging. Conventional methods (emission subtraction) for ACF computation from post-injection scans are suboptimal and require relatively long scan times. We introduce statistical methods based on penalized-likelihood objectives to compute ACFs and then use them to reconstruct lower noise PET emission images from simultaneous transmission/emission scans. Simulations show the efficacy of the proposed methods. These methods improve image quality and SNR of the estimates as compared to conventional methods

[en] In PET, usually the data are precorrected for accidental coincidence (AC) events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for AC events but destroys the Poisson statistics. Furthermore, for transmission tomography the weighted least-squares (WLS) method leads to systematic biases, especially at low count rates. We propose a new open-quotes shiftedclose quotes Poisson (SP) model for precorrected PET data, which properly matches the first and second order moments of the measurement statistics. Using simulations and analytic approximations, we show that estimators based on the open-quotes ordinaryclose quotes Poisson (OP) model for the precorrected data lead to higher standard deviations than the proposed method. Moreover, if one zero-thresholds the data before applying the maximization algorithm, the OP model results in systematic bias. It is shown that the proposed SP model leads to penalized-likelihood estimates free of systematic bias, even for zero-thresholded data. The proposed SP model does not increase the computation requirements compared to OP model and it is robust to errors in the estimates of the AC event rates

[en] We have investigated the improvement in resolution and sensitivity for brain imaging which would result by the addition of a single stationary vertex view to the tomographic data. This method has the practical advantage of being relatively inexpensive and easy to implement. The uniform Cramer Rao bound is a plot of the minimum achievable standard deviation for estimating the pixel intensity as a function of the bias gradient length. Uniform CR bound analysis indicated an improvement in performance when the vertex detector is added, especially for centrally located pixels for which improvement is seen over the useful depth for brain imaging. Simulation experiments were done with a simple six slice phantom and with the Hoffman brain phantom. Visual inspection of the reconstructed images showed improved resolution and noise characteristics over reconstructed images without the vertex data. Quantitatively, substantial reduction in mean square error was observed for a plane close to the vertex detector. Improvement reduced as distance from the vertex detector is increased. Background activities inside the field of view of the vertex detector but not the tomograph were represented by several blobs of activity on a plane lying outside the reconstruction volume. This activity was estimated by 3D spline fitting jointly with the image reconstruction process. Adding the vertex view to conventional brain SPECT should lead to improved cortical imaging, and to moderate improvement for deep structures

[en] This paper presents an image reconstruction method for positron-emission tomography (PET) based on a penalized, weighted least-squares (PWLS) objective. For PET measurements that are precorrected for accidental coincidences, the authors argue statistically that a least-squares objective function is as appropriate, if not more so, than the popular Poisson likelihood objective. The authors propose a simple data-based method for determining the weights that accounts for attenuation and detector efficiency. A non-negative successive over-relaxation (+SOR) algorithm converges rapidly to the global minimum of the PWLS objective. Quantitative simulation results demonstrate that the bias/variance trade-off of the PWLS + SOR method is comparable to the maximum-likelihood expectation-maximization (ML-EM) method (but with fewer iterations), and is improved relative to the conventional filtered backprojection (FBP) method. Qualitative results suggest that the streak artifacts common to the FBP method are nearly eliminated by the PWLS + SOR method, and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over FBP

[en] We present the results of combining volume imaging with the PENN-PET scanner with statistical image reconstruction methods such as the penalized weighted least squares (PWLS) method. The goal of this particular combination is to improve both classification and estimation tasks in PET imaging protocols where image quality is dominated by spatially-variant system responses and/or measurement statistics. The PENN-PET scanner has strongly spatially-varying system behavior due to its volume imaging design and the presence of detector gaps. Statistical methods are easily adapted to this scanner geometry, including the detector gaps, and have also been shown to have improved bias/variance trade-offs compared to the standard filtered-backprojection (FBP) reconstruction method. The PWLS method requires fewer iterations and may be more tolerant of errors in the system model than other statistical methods. We present results demonstrating the improvement in image quality for PWLS image reconstructions of data from the PENN-PET scanner

[en] Since the data sizes in fully 3D PET imaging are very large, iterative image reconstruction algorithms must converge in very few iterations to be useful. One can improve the convergence rate of the conjugate-gradient (CG) algorithm by incorporating preconditioning operators that approximate the inverse of the Hessian of the objective function. If the 3D cylindrical PET geometry were not truncated at the ends, then the Hessian of the penalized least-squares objective function would be approximately shift-invariant, i.e. G'G would be nearly block-circulant, where G is the system matrix. We propose a Fourier preconditioner based on this shift-invariant approximation to the Hessian. Results show that this preconditioner significantly accelerates the convergence of the CG algorithm with only a small increase in computation

[en] As investigators consider more comprehensive measurement models for emission tomography, there will be more choices for the complete-data spaces of the associated expectation-maximization (EM) algorithms for maximum-likelihood (ML) estimation. In this paper, the authors show that EM algorithms based on smaller complete-data spaces will typically converge faster. They discuss two practical applications of those concepts: (1) the ML-IA and ML-IB image reconstruction algorithms of Politte and Snyder which are based on measurement models that account for attenuation and accidental coincidences in positron-emissions tomography (PET), and (2) the problem of simultaneous estimation of emission and transmission parameters. Although the PET applications may often violate the necessary regularity conditions, their analysis predicts heuristically that the ML-IB algorithm, which has a smaller complete-data space, should converge faster than ML-IA. This is corroborated by the empirical findings

[en] Single Photon Emission Computed Tomography (SPECT) provides a potential to perform in vivo quantification of the radioactivity and dose distributions in the process of evaluating radiopharmaceuticals. The inherent modest resolution in SPECT impedes the potential of accurate quantification. Previously, we investigated a joint estimation approach for combining SPECT functional information with high resolution, structurally correlated MRI anatomical information to improve the accuracy of SPECT quantification, and the computer simulation results showed that this approach can exploit MRI region information that matches the SPECT functional information and to reduce artifacts caused by mismatched MRI anatomical information. In this paper, we further describe the experimental evaluation of the joint estimation approach using actual SPECT and MRI imaging with an animal-sized phantom. We will describe practical details in applying the joint estimation approach and present the experimental evaluation results of quantitative analysis

[en] The inadequacy of the maximum-likelihood criterion for emission image reconstruction has spurred the development of several regularization methods. Despite the spatial variance of medical images, most of the proposed methods are spatially invariant. This paper reports an investigation of a spatially-variant penalized-likelihood method to tomographic image reconstruction based on a weighted Gibbs penalty. the penalty weights are determined form structural side information, such as the locations of anatomical boundaries in high-resolution magnetic resonance images. such side information will be imperfect in practice, and a simple simulation demonstrates the importance of accounting for the errors in boundary locations. We discuss methods for prescribing the penalty weights when the side information is noisy. simulation results suggest that even imperfect side information is useful for guiding spatially-variant regularization

[en] The ordered subsets EM (OSEM) algorithm has enjoyed considerable interest for emission image reconstruction due to its acceleration of the original EM algorithm and ease of programming. The transmission EM reconstruction algorithm converges very slowly and is not used in practice. In this paper, we introduce a simultaneous update algorithm called separable paraboloidal surrogates (SPS) that converges much faster than the transmission EM algorithm. Furthermore, unlike the 'convex algorithm' for transmission tomography, the proposed algorithm is monotonic even with nonzero background counts. We demonstrate that the ordered subsets principle can also be applied to the new SPS algorithm for transmission tomography to accelerate 'convergence', albeit with similar sacrifice of global convergence properties as for OSEM. We implemented and evaluated this ordered subsets transmission (OSTR) algorithm. The results indicate that the OSTR algorithm speeds up the increase in the objective function by roughly the number of subsets in the early iterates when compared to the ordinary SPS algorithm. We compute mean square errors and segmentation errors for different methods and show that OSTR is superior to OSEM applied to the logarithm of the transmission data. However, penalized-likelihood reconstructions yield the best quality images among all other methods tested. (author)