Monotonic Algorithms for Transmission Tomography

Presents a framework for designing fast and monotonic algorithms for transmission tomography penalized-likelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the log likelihood, Due to the form of the log-likelihood function it is possible to find low curvature surrogate functions that guarantee monotonicity. Unlike previous methods, the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log likelihood that arises due to background events, such as scatter and random coincidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the problem is simplified at each iteration, the CPU time is less than that of current algorithms which directly minimize the objective, yet the convergence rate is comparable. The simplicity, monotonicity, and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real and simulated PET transmission scans.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85831/1/Fessler83.pd

Image Recovery Using Partitioned-Separable Paraboloidal Surrogate Coordinate Ascent Algorithms

Iterative coordinate ascent algorithms have been shown to be useful for image recovery, but are poorly suited to parallel computing due to their sequential nature. This paper presents a new fast converging parallelizable algorithm for image recovery that can be applied to a very broad class of objective functions. This method is based on paraboloidal surrogate functions and a concavity technique. The paraboloidal surrogates simplify the optimization problem. The idea of the concavity technique is to partition pixels into subsets that can be updated in parallel to reduce the computation time. For fast convergence, pixels within each subset are updated sequentially using a coordinate ascent algorithm. The proposed algorithm is guaranteed to monotonically increase the objective function and intrinsically accommodates nonnegativity constraints. A global convergence proof is summarized. Simulation results show that the proposed algorithm requires less elapsed time for convergence than iterative coordinate ascent algorithms. With four parallel processors, the proposed algorithm yields a speedup factor of 3.77 relative to single processor coordinate ascent algorithms for a three-dimensional (3-D) confocal image restoration problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86024/1/Fessler72.pd

Monte-Carlo simulations and image reconstruction for novel imaging scenarios in emission tomography

AbstractEmission imaging incorporates both the development of dedicated devices for data acquisition as well as algorithms for recovering images from that data. Emission tomography is an indirect approach to imaging. The effect of device modification on the final image can be understood through both the way in which data are gathered, using simulation, and the way in which the image is formed from that data, or image reconstruction. When developing novel devices, systems and imaging tasks, accurate simulation and image reconstruction allow performance to be estimated, and in some cases optimized, using computational methods before or during the process of physical construction. However, there are a vast range of approaches, algorithms and pre-existing computational tools that can be exploited and the choices made will affect the accuracy of the in silico results and quality of the reconstructed images. On the one hand, should important physical effects be neglected in either the simulation or reconstruction steps, specific enhancements provided by novel devices may not be represented in the results. On the other hand, over-modeling of device characteristics in either step leads to large computational overheads that can confound timely results. Here, a range of simulation methodologies and toolkits are discussed, as well as reconstruction algorithms that may be employed in emission imaging. The relative advantages and disadvantages of a range of options are highlighted using specific examples from current research scenarios

Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis

Relevance of accurate Monte Carlo modeling in nuclear medical imaging

Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. This paper presents derivation and methodological basis for this approach and critically reviews their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed

Incorporating accurate statistical modeling in PET: reconstruction for whole-body imaging

Tese de doutoramento em Biofísica, apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2007The thesis is devoted to image reconstruction in 3D whole-body PET imaging. OSEM ( Ordered Subsets Expectation maximization ) is a statistical algorithm that assumes Poisson data. However, corrections for physical effects (attenuation, scattered and random coincidences) and detector efficiency remove the Poisson characteristics of these data. The Fourier Rebinning (FORE), that combines 3D imaging with fast 2D reconstructions, requires corrected data. Thus, if it will be used or whenever data are corrected prior to OSEM, the need to restore the Poisson-like characteristics is present. Restoring Poisson-like data, i.e., making the variance equal to the mean, was achieved through the use of weighted OSEM algorithms. One of them is the NECOSEM, relying on the NEC weighting transformation. The distinctive feature of this algorithm is the NEC multiplicative factor, defined as the ratio between the mean and the variance. With real clinical data this is critical, since there is only one value collected for each bin the data value itself. For simulated data, if we keep track of the values for these two statistical moments, the exact values for the NEC weights can be calculated. We have compared the performance of five different weighted algorithms (FORE+AWOSEM, FORE+NECOSEM, ANWOSEM3D, SPOSEM3D and NECOSEM3D) on the basis of tumor detectablity. The comparison was done for simulated and clinical data. In the former case an analytical simulator was used. This is the ideal situation, since all the weighting factors can be exactly determined. For comparing the performance of the algorithms, we used the Non-Prewhitening Matched Filter (NPWMF) numerical observer. With some knowledge obtained from the simulation study we proceeded to the reconstruction of clinical data. In that case, it was necessary to devise a strategy for estimating the NEC weighting factors. The comparison between reconstructed images was done by a physician largely familiar with whole-body PET imaging

Investigation of the Effects of Image Signal-to-Noise Ratio on TSPO PET Quantification of Neuroinflammation

Neuroinflammation may be imaged using positron emission tomography (PET) and the tracer [11C]-PK11195. Accurate and precise quantification of 18 kilodalton Translocator Protein (TSPO) binding parameters in the brain has proven difficult with this tracer, due to an unfavourable combination of low target concentration in tissue, low brain uptake of the tracer and relatively high non-specific binding, all of which leads to higher levels of relative image noise. To address these limitations, research into new radioligands for the TSPO, with higher brain uptake and lower non-specific binding relative to [11C]-PK11195, is being conducted world-wide. However, factors other than radioligand properties are known to influence signal-to-noise ratio in quantitative PET studies, including the scanner sensitivity, image reconstruction algorithms and data analysis methodology. The aim of this thesis was to investigate and validate computational tools for predicting image noise in dynamic TSPO PET studies, and to employ those tools to investigate the factors that affect image SNR and reliability of TSPO quantification in the human brain. The feasibility of performing multiple (n≥40) independent Monte Carlo simulations for each dynamic [11C]-PK11195 frame- with realistic modelling of the radioactivity source, attenuation and PET tomograph geometries- was investigated. A Beowulf-type high performance computer cluster, constructed from commodity components, was found to be well suited to this task. Timing tests on a single desktop computer system indicated that a computer cluster capable of simulating an hour-long dynamic [11C]-PK11195 PET scan, with 40 independent repeats, and with a total simulation time of less than 6 weeks, could be constructed for less than 10,000 Australian dollars. A computer cluster containing 44 computing cores was therefore assembled, and a peak simulation rate of 2.84x105 photon pairs per second was achieved using the GEANT4 Application for Tomographic Emission (GATE) Monte Carlo simulation software. A simulated PET tomograph was developed in GATE that closely modelled the performance characteristics of several real-world clinical PET systems in terms of spatial resolution, sensitivity, scatter fraction and counting rate performance. The simulated PET system was validated using adaptations of the National Electrical Manufacturers Association (NEMA) quality assurance procedures within GATE. Image noise in dynamic TSPO PET scans was estimated by performing n=40 independent Monte Carlo simulations of an hour-long [11C]-PK11195 scan, and of an hour- long dynamic scan for a hypothetical TSPO ligand with double the brain activity concentration of [11C]-PK11195. From these data an analytical noise model was developed that allowed image noise to be predicted for any combination of brain tissue activity concentration and scan duration. The noise model was validated for the purpose of determining the precision of kinetic parameter estimates for TSPO PET. An investigation was made into the effects of activity concentration in tissue, radionuclide half-life, injected dose and compartmental model complexity on the reproducibility of kinetic parameters. Injecting 555 MBq of carbon-11 labelled TSPO tracer produced similar binding parameter precision to 185 MBq of fluorine-18, and a moderate (20%) reduction in precision was observed for the reduced carbon-11 dose of 370 MBq. Results indicated that a factor of 2 increase in frame count level (relative to [11C]-PK11195, and due for example to higher ligand uptake, injected dose or absolute scanner sensitivity) is required to obtain reliable binding parameter estimates for small regions of interest when fitting a two-tissue compartment, four-parameter compartmental model. However, compartmental model complexity had a similarly large effect, with the reduction of model complexity from the two-tissue compartment, four-parameter to a one-tissue compartment, two-parameter model producing a 78% reduction in coefficient of variation of the binding parameter estimates at each tissue activity level and region size studied. In summary, this thesis describes the development and validation of Monte Carlo methods for estimating image noise in dynamic TSPO PET scans, and analytical methods for predicting relative image noise for a wide range of tissue activity concentration and acquisition durations. The findings of this research suggest that a broader consideration of the kinetic properties of novel TSPO radioligands, with a view to selection of ligands that are potentially amenable to analysis with a simple one-tissue compartment model, is at least as important as efforts directed towards reducing image noise, such as higher brain uptake, in the search for the next generation of TSPO PET tracers

Iterative Reconstruction of Cone-Beam Micro-CT Data

The use of x-ray computed tomography (CT) scanners has become widespread in both clinical and preclinical contexts. CT scanners can be used to noninvasively test for anatom- ical anomalies as well as to diagnose and monitor disease progression. However, the data acquired by a CT scanner must be reconstructed prior to use and interpretation. A recon- struction algorithm processes the data and outputs a three dimensional image representing the x-ray attenuation properties of the scanned object. The algorithms in most widespread use today are based on filtered backprojection (FBP) methods. These algorithms are rela- tively fast and work well on high quality data, but cannot easily handle data with missing projections or considerable amounts of noise. On the other hand, iterative reconstruction algorithms may offer benefits in such cases, but the computational burden associated with iterative reconstructions is prohibitive. In this work, we address this computational burden and present methods that make iterative reconstruction of high-resolution CT data possible in a reasonable amount of time. Our proposed techniques include parallelization, ordered subsets, reconstruction region restriction, and a modified version of the SIRT algorithm that reduces the overall run-time. When combining all of these techniques, we can reconstruct a 512 × 512 × 1022 image from acquired micro-CT data in less than thirty minutes