In this work, we have created a reconstruction framework to reconstruct 4D time series images from PET systems of arbitrary geometry. This investigation is a component of the overarching theme of designing application specific PET imaging devices, adaptable to the imaging target and is a precursor to optimizing the design of PET systems.
In developing this framework, we have learned that the expectation-maximization algorithm [21] is robust in its ability to reconstruct artifact free images under various geometrical
arrangements of detectors of varying sizes, provided that there is complete sampling of the basis functions in the image. In the absence of complete sampling, artifacts are introduced.
Since these artifacts must be addressed through an external signal or prior understanding that is dependent of system geometry on a case by case basis, we have not attempted to correct for such artifacts.
Another group has helped advance the field along a similar direction [30]. However, their goal requires further investigation such as the optimization of the framework, particularly the automatic computation of symmetries, choice of subsets, and normalization components.
These choices are vital for the framework to be adaptable to a large subset of PET geometries, while simultaneously being able to reconstruct in an efficient manner.
We would like to also note that further improvements to such a framework is possible.
Although the framework can model a large variety of existing systems with different crystal size and position, we have not accounted for Time of Flight PET or Depth of Interaction (DOI) detectors. Furthermore, more accurate system matrices could potentially provide better quantification accuracy. In this regard, we have not modeled positron range correction or Point Spread Function (PSF) deblurring. These are left as future improvements to the framework.
A major limitation of the current framework is that it is built for static systems with a fixed system matrix. A research direction that we are currently exploring has movable detectors in a dynamic geometry that can be optimized for the subject of interest.
For the OS-EM algorithm, we have chosen a particular subset selection strategy and the log-cosh prior. The general design of the framework allows for studying other subset strategies and better regularizers. Some of the systems have non-uniform image resolution, and could benefit from a spatially varying prior[72]. Choosing a geometry independent subset strategy and prior is beyond the scope of this study.
The current framework can handle very large system matrices and complicated systems.
Although memory usage and computational time is high for accurate image reconstruction, Moore’s law predicts faster systems and lower memory cost in the future. Yet, there are advantages to optimizing the memory usage and convergence rate as a function of compu-tational time. There is scope for further research for geometry independent memory/speed
optimization. Other groups have shown progress in these areas, which can be potentially included in our framework. For instance, our approach of reducing the memory requirement is an extension of the existing approach of manual symmetry computation. This is a loss-less form of compression. More gains in memory can be made designing a lossy compression scheme, capable of trading of accuracy for memory usage [94]. With respect to computational speed, range-domain decomposition methods[51] and optimization transfer[2, 42] could be potentially explored.
Currently, a significant amount of work has been done by other groups to port reconstruction codes written for x86 architecture to highly parallel Graphic Processor Units (GPU) with simple cores. The approach is justified in the projection process in reconstruction performs the same instructions on multiple data simultaneously. Adapting x86 code to GPU requires simplification and sectioning of the system matrix. In order to maintain the accuracy of the reconstruction, they are not pursued in this work. More importantly, future computing architectures such as the Intel Many Integrated Core (MIC) combines the highly parallel nature of GPUs with the ability to run x86 code. Also, toolkits that convert generic C/C++
code to run on GPU architectures already exist.
5.6 Conclusion
We have developed an accurate image reconstruction framework for four dimensional coin-cidence data acquired from unconventional positron emission tomography systems. We are focused on designing optimal application-specific PET systems. The reconstruction frame-work helps validate our hypothesis relating to different application areas, as well as optimize the design of the systems.
Although traditional reconstruction has focused on ring systems and processing data using sinograms, we have moved away from the approach. We have generalized some of the tradi-tional concepts in PET reconstruction to model systems of arbitrary geometry, with crystals of different sizes and materials. Lines of Response between different types of crystals which were treated differently in previous works are approached through the same mechanism.
Modeling of unknown components that are to be estimated using the normalization pro-cedure is made trivial given an understanding of the unknown variables and the lines of response that they affect.
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