Performance evaluation of MAP algorithms with different penalties, object geometries and noise levels

A new algorithm (LBFGS-B-PC) which combines ideas of two existing convergent reconstruction algorithms, relaxed separable paraboloidal surrogate (SPS) and limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (LBFGS-B), is proposed. Its performance is evaluated in terms of log-posterior value and regional recovery ratio. The results demonstrate the superior convergence speed of the proposed algorithm to relaxed SPS and LBFGS-B, regardless of the noise level, activity distribution, object geometry, and penalties

Performance improvement and validation of a new MAP reconstruction algorithm

We previously proposed a fast maximum a posteriori (MAP) algorithm, limited-memory Broyden-Fletcher-Goldfarb- Shanno with boundary constrains (LBFGS-B-PC), combining LBFGS-B with diagonal preconditioning. Previous results have shown in simulations that it converges using around 40 projections independent of many factors. The aim of this study is to improve the algorithm further by using a better initial image and a modified preconditioner that is less sensitive to noise and data scale. By initializing the algorithm with the best initial image (one full iteration of OSEM with 35 subsets), ROI values can converge almost twice as fast for the same computation time. Moreover, the new preconditioner makes the performance more consistent between high and low count data sets. In addition, we have found a means to choose the stopping criteria to reach a desired level of quantitative accuracy in the reconstructed image. Based on the results with patient data, the optimized LBFGS-B-PC shows promise for clinical imaging

Penalized PET/CT Reconstruction Algorithms With Automatic Realignment for Anatomical Priors

Two algorithms for solving misalignment issues in penalized PET/CT reconstruction using anatomical priors are proposed. Both approaches are based on a recently published joint motion estimation and image reconstruction method. The first approach deforms the anatomical image to align it with the functional one while the second approach deforms both images to align them with the measured data. Our current implementation alternates between alignment estimation and image reconstruction. We have chosen parallel level sets (PLSs) as a representative anatomical penalty, incorporating a spatially variant penalty strength. The performance was evaluated using simulated nontime-of-flight data generated with an XCAT phantom in the thorax region. We used the attenuation map in the anatomical prior. The results demonstrated that both methods can estimate the misalignment and deform the anatomical image accordingly. However, the performance of the first approach depends highly on the workflow of the alternating process. The second approach shows a faster convergence rate to the correct alignment and is less sensitive to the workflow. The presence of anatomical information improves the convergence rate of misalignment estimation for the second approach but slow it down for the first approach. Both approaches show improved performance in misalignment estimation as the data noise level decreases

Algorithms for Solving Misalignment Issues in Penalized PET/CT Reconstruction Using Anatomical Priors

In dual-modality systems, using anatomical priors has been shown to improve image quality and quantification in emission tomography. However, alignment between the functional and anatomical images is crucial. In this study, we propose two algorithms for solving misalignment issues. Both approaches are based on a recently published joint motion estimation and image reconstruction method. The first approach deforms the anatomical image to align it with the functional one while the second approach deforms both images to align them with the measured data. Our current implementation uses alternates between image reconstruction and alignment estimation. To evaluate the potential of these approaches, we have chosen Parallel Level Sets (PLS) as a representative anatomical penalty since it has shown promising results in literature, incorporating a spatially-variant penalty strength to achieve uniform local contrast and fast convergence rate. The performance evaluation was achieved by using simulated non-TOF data generated with an XCAT phantom in the thorax region. We used the attenuation image in the anatomical prior. The results demonstrated that both methods are able to estimate the misalignment and deform the anatomical image accordingly when a proper workflow for the alternating optimization is applied. However, the performance of the first approach depends highly on the workflow of the alternating process. In contrast, the second approach shows the ability to converge to the correct alignment faster than the first approach does, independent of the workflow. Our results indicate that it is possible to align functional and anatomical information, enabling the use of anatomical priors in practice

Collimator design for a clinical brain SPECT/MRI insert

This project's goal is to design a SPECT insert for a clinical MRI system for simultaneous brain SPECT/MR imaging. We assume the stationary SPECT insert will consist of two rings of ∼5x5-cm SiPM-based detectors insensitive to magnetic fields, with 0.8-mm intrinsic resolution. The maximum diameter is 44.5 cm, the minimum diameter is 33 cm to accommodate the patient and MRI receive/transmit coil, and the FOV has a 20 cm diameter. We have compared eight collimator designs: single-, 2x2-, 3x3- and 5+2½- pinhole, and single-, 2-, 3- and 1+2½-slit slit-slat, where ½-pinholes/slits are shared between two detectors. Analytical geometric efficiency was calculated for an activity distribution corresponding to a human brain and a target resolution of 10 mm FWHM at the centre of the FOV. Noise-free data were simulated with and without depth-of-interaction (DOI) information, and reconstructed for uniform, Defrise, Derenzo, and Zubal brain phantoms. For DOI it is assumed that the crystal's first and second half can be differentiated. Comparing the multi-pinhole and multi-slit slit-slat collimators, the former gives better reconstructed uniformity and trans-axial resolution, while the latter gives better axial resolution. Although the 2x2-pinhole and 2-slit designs give the highest sensitivities, they result in a sub-optimal utilization of the detector FOV. The best options are therefore the 5+2½-pinhole and the 1+2½-slit systems, with sensitivities of 4.9*10–4 and 4.0*10–4, respectively. The brain phantom reconstructions with multi-pinhole collimator are superior as compared to slit-slat, especially in terms of symmetry and realistic activity distribution. DOI information reduces artefacts and improves uniformity in geometric phantoms, although the difference is small for the brain phantom. These results favour a multi-pinhole configuration

Maximum-likelihood estimation of emission and attenuation images in 3D PET from multiple energy window measurements

This study explores the feasibility of incorporating energy information into a maximum-likelihood reconstruction of activity and attenuation (MLAA) framework. The attenuation and activity distributions were reconstructed from multiple energy window data, and a scatter function was added to the system model of the algorithm. The proposed energy-based method (MLAA-EB) was evaluated with simulated 3D phantom data, using the geometry and characteristics of a Siemens mMR PET-MR scanner. Results showed that the proposed algorithm is able to compensate for errors in the activity image caused by the incorrect assignment of attenuation values to the segmented MR. This is effective for small objects only, for large objects further solutions need to be found

Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning

OAPA This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden- Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGSB), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGSB and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGSB- PC shows promise for clinical application

Respiratory Motion Correction in Dynamic PET with a Single Attenuation Map

In addition to static tracer uptake values used routinely in clinical facilities, PET imaging can provide useful information on tracer kinetics via the use of dynamic acquisitions where a set of time frames are acquired starting from the injection/inhalation of the radiotracer. In lung studies, kinetic parameters, estimated from compartmental modelling, are however affected by respiratory motion. When only one attenuation image is available, most existing motion compensation strategies are not appropriate for the initial short time frames, especially as the activity distribution changes rapidly over the early part of the dynamic acquisition. This work presents a preliminary study to handle respiratory motion using a two-step process that uses gated dynamic data as input. We first use joint reconstruction of activity and motion on the entire gated PET data to estimate deformation fields. This allows the subsequent reconstruction of each time frame separately with motion compensation. We present results comparing on one hand the compartment model fit residuals with and without respiratory motion compensation and on the other hand the diaphragm position in non-attenuation corrected images and from this method

Joint reconstruction of activity and attenuation in dynamic PET

Joint reconstruction of attenuation and emission in positron emission tomography (PET) using the maximum likelihood activity and attenuation estimation (MLAA) algorithm was proposed in the past. However, cross-talk between the activity and attenuation estimation limits the usefulness of MLAA for PET data without time-of-flight (TOF) information. This work introduces dynamic MLAA (dMLAA), an extension of the MLAA algorithm for dynamic data, to jointly reconstruct the activity distributions and a single attenuation map. The hypothesis is that using information from multiple dynamic emission frames may improve the estimated attenuation map compared to using static PET data. Preliminary results using dMLAA algorithm showed that use of multiple dynamic emission frames slightly improves the reconstructed attenuation map (especially in bones, cavities and lesion area) compared to using a single emission frame. However, without TOF, the reconstructed map still suffers from ill-posedness of the problem despite the additional dynamic information. The reconstruction may be improved for tracers that present a higher inter- and intra-dynamic frame contrast and edge variability

Joint Activity/Attenuation Reconstruction in SPECT Using Photopeak and Scatter Sinograms

This work presents a joint activity/attenuation reconstruction method in SPECT, based on the maximisation of the scatter and non-scatter data joint log-likelihood. The activity image is updated with standard expectation maximisation (EM) whereas the attenuation is updated with a quasi-Newton line-search. Results on simulation demonstrates that the utilisation of scatter considerably reduces the ill-posedness of the initial reconstruction problem with non-scatter counts only. Results on phantom data show that using scatter enables myocardial reconstruction similar to an EM reconstruction with CT attenuation correctio