Purpose:
In iterative positron emission tomography (PET) image reconstruction, the statistical variability of the PET data precorrected for random coincidences or acquired in sufficiently high count ...rates can be properly approximated by a Gaussian distribution, which can lead to a penalized weighted least-squares (PWLS) cost function. In this study, the authors propose a proximal preconditioned gradient algorithm accelerated with ordered subsets (PPG-OS) for the optimization of the PWLS cost function and develop a framework to incorporate boundary side information into edge-preserving total variation (TV) and Huber regularizations.
Methods:
The PPG-OS algorithm is proposed to address two issues encountered in the optimization of PWLS function with edge-preserving regularizers. First, the second derivative of this function (Hessian matrix) is shift-variant and ill-conditioned due to the weighting matrix (which includes emission data, attenuation, and normalization correction factors) and the regularizer. As a result, the paraboloidal surrogate functions (used in the optimization transfer techniques) end up with high curvatures and gradient-based algorithms take smaller step-sizes toward the solution, leading to a slow convergence. In addition, preconditioners used to improve the condition number of the problem, and thus to speed up the convergence, would poorly act on the resulting ill-conditioned Hessian matrix. Second, the PWLS function with a nondifferentiable penalty such as TV is not amenable to optimization using gradient-based algorithms. To deal with these issues and also to enhance edge-preservation of the TV and Huber regularizers by incorporating adaptively or anatomically derived boundary side information, the authors followed a proximal splitting method. Thereby, the optimization of the PWLS function is split into a gradient descent step (upgraded by preconditioning, step size optimization, and ordered subsets) and a proximal mapping associated with boundary weighted TV and Huber regularizers. The proximal mapping is then iteratively solved by dual formulation of the regularizers.
Results:
The convergence performance of the proposed algorithm was studied with three different diagonal preconditioners and compared with the state-of-the-art separable paraboloidal surrogates accelerated with ordered-subsets (SPS-OS) algorithm. In simulation studies using a realistic numerical phantom, it was shown that the proposed algorithm depicts a considerably improved convergence rate over the SPS-OS algorithm. Furthermore, the results of bias-variance and signal-to-noise evaluations showed that the proposed algorithm with anatomical edge information depicts an improved performance over conventional regularization. Finally, the proposed PPG-OS algorithm is used for image reconstruction of a clinical study with adaptively derived boundary edge information, demonstrating the potential of the algorithm for fast and edge-preserving PET image reconstruction.
Conclusions:
The proposed PPG-OS algorithm shows an improved convergence rate with the ability of incorporating additional boundary information in regularized PET image reconstruction.
The Ingenuity TF PET/MR is a newly developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. Due to the magnetic field, spatial ...resolution in PET could potentially be affected. As such, it is important to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies. An array of 12×7 printed point sources was scanned for 120 minutes to sample the spatially variant PSF with the MR magnet on and the reconstructed data (blob-based LOR-RAMLA) were fitted in image space with a double 3-D Gaussian mixture model to derive parameters of interest. Based on the analysis, the axial resolution was found to be the least variant (up to 5.7mm) followed by the tangential (up to 6.4mm) and the radial (up to 6.9mm). The radial and tangential components were found to be variant under radial transformations and almost invariant under axial transformation. However, this radial dependency was found to be minimal with the resolution degrading only by 2.5mm towards the edge of the radial FOV. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/re-binned enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. To this extent, blob parameters used during image reconstruction could be further optimized to improve the system's resolution characteristics.
Direct application of the expectation maximisation (EM) algorithm to the spatiotemporal maximum likelihood problem results in a convenient separation of the image based problem from the projection ...based problem. This enables any spatiotemporal 4D image model to be incorporated into MLEM image reconstruction with relative ease, only requiring tailored calculation of the fitting weights. As a preliminary example, assessment using direct estimation of spectral analysis coefficients is presented, exploiting an image based non-negative least squares algorithm, where a specially-weighted least squares update is equivalent to the required update towards the maximum likelihood estimate. The proposed approach demonstrates a reduced root mean square error (RMSE) in the estimates of volume of distribution. Future work will include the exploration of alternative spatiotemporal models.
Positron emission tomography (PET) is a powerful and highly specialised imaging modality that has the inherent ability to detect and quantify changes in the bio-distribution of an intravenously ...administered radio-labelled tracer, through dynamic image acquisition of the system under study. By modelling the temporal distribution of the tracer, parameters of interest regarding specific biological processes can be derived. Traditionally parameter estimation is done by first reconstructing a set of dynamic images independently, followed by kinetic modelling, leading to parameters of reduced accuracy and precision. Furthermore only simple geometrical models are used during image reconstruction to model the mapping between the image space and the data space, leading to images of reduced resolution. This thesis attempts to address some of the problems associated with the current methodology, by implementing and evaluating new spatiotemporal image reconstruction strategies in oncology PET/CT imaging, with simulated, phantom and real data. More specifically this thesis is concerned with iterative reconstruction techniques, the incorporation of resolution recovery and kinetic modelling strategies within the image reconstruction process and the application of such methods in perfusion 15OH2O imaging. This work is mainly based upon 2 whole body PET/CT scanners, the Siemens Biograph 6 B-HiRez and TruePoint TrueV, but some aspects of this work were also implemented for the High resolution research tomograph (HRRT).
Direct parametric image reconstruction has the potential to reduce variance in parameter estimates when applied to PET/CT data. One complication when estimating parametric maps in the body is the ...difficulty of finding one single model to describe all the different kinetics in the field of view (FOV). Contrary to the post-reconstruction kinetic analysis though, any errors (bias) from the discrepancy between the model and the observed kinetics in the direct 4D reconstruction can potentially propagate spatially from unimportant areas to areas of interest. In this work we investigate this effect on simulated 4-D datasets based on a digital body phantom. Different realistic cases were simulated including differential input functions in the FOV and organs with different kinetics. Micro-parameters (K 1 , k 2 ,Vd, bv) where estimated using a newly proposed spatiotemporal 4D image reconstruction algorithm as well as using post-reconstruction kinetic analysis on noiseless and noisy datasets simulating 15 O H 2 O kinetics in the body. Bias analysis both in noiseless and noisy data showed a bias from badly modelled areas spatially propagates to other regions of interest in the direct reconstruction. Critically though under noisy conditions even with the bias propagation, the direct reconstruction method still outperforms the conventional post-reconstruction methodology. Nevertheless there is a need to ensure that appropriate models are chosen to describe the kinetics in the entire FOV with approaches such as data-driven adaptive kinetic modelling worth exploring.
Abdominal and thoracic 18 FFDG PET/CT imaging is routinely used in clinical practice and drug development but parametric imaging based on full kinetic analysis is rarely used due to noise induced ...bias and variance in kinetic parameters and analysis is usually restricted to semi-quantitative indices. Direct parametric estimation using 4D image reconstruction can potentially provide parametric maps of reduced bias and variance but little or no evaluation has been done in the body. Previous studies have demonstrated that body 18 FFDG PET/CT imaging can benefit from these methods but analysis was restricted to macroparameters of interest. In work, we implement and apply a recently proposed direct 4-D algorithm using a 2 tissue compartment model on simulated and real oncology 18 FFDG PET/CT data to directly estimate microparameters of interest and assess potential improvements over the traditional post-reconstruction kinetic analysis. Results on the simulated data suggest clear reduction in bias for K 1 , k 2 and blood volume and less for k 3 . Similarly, variance reduction was observed for K 1 , k 2 , k 3 and K i and less for blood volume. Evaluation on patient data demonstrated similar improvements using the direct 4-D method in agreement with simulations.
Methods for adaptively fitting kinetic models to image data are explored. In conducting this fitting two goals are set: 1) that good fits are obtained for all image voxels; and 2) that where a ...primary biologically based model is appropriate, this model is used. The first goal is obtained through the inclusion of a more general secondary model. The second goal is achieved through the penalisation of estimates from this secondary model with the weighting of this penalisation optimised using generalised cross validation. The result is a modelling scheme where the secondary model is adaptively included for voxels that the primary model is unable to fit. The envisaged application is in 4D (space and time) reconstruction to prevent spatial propagation of errors from regions where a primary model is not appropriate. An evaluation of reconstructed clinical data using a dataset with challenging kinetics has been conducted. Application to the clinical dataset showed promising results with the modelling scheme able to fit kinetics associated with activity in the region of the injection site veins, the right ventricle, right atrium and the gall bladder. The method requires the careful selection of the secondary model and further work is needed to optimise this selection and evaluate the benefit for 4D reconstruction.
Direct 4D image reconstruction algorithms can improve kinetic parameter precision and accuracy in dynamic PET/CT body imaging but in contrast to post-reconstruction kinetic analysis, errors in badly ...modeled regions will spatially propagate to regions which are well modeled. To reduce error propagation from erroneous model fits, we propose a new approach to direct 4D image reconstruction by incorporating a newly proposed kinetic modeling strategy. This uses a secondary model to allow a less constrained model fit in regions where an erroneous kinetic model is used and adaptively include a portion of the residuals back into the image, whilst preserving the primary model characteristics in other well modeled regions. Using a digital 4-D phantom to simulate 15 O-H 2 O kinetics, we demonstrate substantial bias reduction due to propagation in all kinetic parameters using the proposed 4-D method. Under noisy conditions improvements in bias due to propagation are obtained at the expense of a small increase in bias due to noise and selective inclusion of residuals coming from erroneous kinetic modeling, as opposed to noise, becomes more challenging. However, the overall bias is reduced with improvements depending on the proximity of regions of interest to badly modeled regions and the choice of the secondary model space.
Accurate characterisation of the point spread function across the entire field of view is crucial in order to account for spatially dependent factors that degrade the resolution of the reconstructed ...images. The HRRT users community resolution modelling reconstruction software includes a shift-invariant resolution kernel, which leads to transaxially non-uniform resolution recovery. In this work we have developed a spatially-variant image-based resolution modelling reconstruction dedicated to the HRRT scanner, using an experimentally measured shift-variant resolution kernel. Application of the newly developed resolution modelling reconstruction on both phantom and clinical data demonstrated improvements both in contrast and resolution recovery, particularly for those regions that are close to the edges of the field of view, with almost uniform resolution recovery across the entire transverse field of view. In addition, because the newly measured resolution kernel is slightly broader with wider tails, compared to the deliberately conservative kernel employed in the HRRT users community software, the reconstructed images appear to have not only improved contrast recovery, but also better noise characteristics, at the expense of minor development of ringing (i.e. Gibbs) artefacts.
