Abstract
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Objectives: Iterative tomographic reconstruction typically relies on a single objective function, often containing a data fidelity and a regularization term. These approaches require fixing the tradeoff prior to reconstruction and lead to a single optimal solution that satisfies the fixed joint objective. In PET practice, images are used for multiple tasks, such as quantitation and detection, and a single image is rarely optimal for multiple tasks. In this work, we explore the novel use of multi-objective optimization to identify a set of images that could be optimal for more than one task.
Methods: We developed a genetic algorithm to evolve a set of solutions that satisfies two objectives. We defined the objectives as the conventional Poisson log-likelihood function, typically favorable for quantitation, and a generalized scan-statistic model, to reflect goodness at detecting 1 cm features. The genetic algorithm uses a suite a new mutation, crossover, and selection operations at each iteration; the algorithm uses non-dominated sorting to identify candidate parents for the next generation. This method was applied to simulated PET data of the chest with a single pulmonary nodule. We evolved a population of 100 PET images to determine the Pareto optimal front—In essence, the set of PET images for which none the objective function values can be improved without reducing the opposing objective function. We compared this approach to a conventional approach for trading off performance based on the maximum likelihood solution with increasing explicit regularization through post-reconstruction filtering.
Results: In the simulation evaluation, the genetic algorithm successful evolved a set of solutions to improve performance in terms of the quantitation and detection objectives. The images along this front of solutions visually demonstrate the tradeoffs of the two objectives, with images at one extreme of the front having high levels of noise with accurate quantitation and images at the other extreme having lower noise levels with visually improved detection. In comparison to conventional post-reconstruction smoothing, the set of solutions from the genetic algorithm was optimal for both the quantitation and detection objectives.
Conclusions: To the best of our knowledge, this is the first work to apply multi-objective optimization to PET image reconstruction. The proposed approach could be used to generate a set of solutions that balance the tradeoff of the performance of different tasks. Furthermore, considering the genetic algorithm does not require differentiable objective functions, this work allows for the use of generalized objective functions that may be more expressive of task performance such as detectability of fixed size features.