Iterative PET Reconstruction Algorithms followed by Non-Local Means Denoising for Improved Quantitative Imaging

Introduction: To test the use of non-local means (NLM) as a method to improve the quantitative performance of various iterative PET reconstruction algorithms using a python-based framework.

Methods: Realistic simulated PET images were generated from first principles using radiopharmaceutical maps coupled to attenuation maps. We specifically focused on modeling of three distinct regions: lesions, liver, and background. Noise was modeled by generating a total number of decays from each pixel that followed a Poisson distribution with mean proportional to the true radiopharmaceutical concentration. To account for attenuation, sinograms were generated using only detected coincidence events.

To obtain quantitative images that provide an estimate of the radiopharmaceutical, attenuation effects present in the sinogram were removed through normalization by a probability map (obtained through a corresponding attenuation map). Sinograms were then used as input for a variety of iterative PET image reconstruction algorithms from the python library TomoPy. Methods included the analytical reconstruction technique (ART), the simultaneous iterative reconstructive technique (SIRT), the total variation reconstruction technique (TV), and variations of maximum-likelihood expectation maximum (MLEM) and ordered-subset expectation maximum (OSEM), including those with linear and quadratic penalty terms. With increasing iterations, noise-bias trade-off curves were generated for different algorithms, enabling comparison between different methods. The results for the different reconstruction algorithms were compared with increasing iterations using noise-bias trade-off curves.

An NLM framework for denoising was applied to generate images at each stage of the iterative process, yielding updated noise-bias trade-off curves. The purpose of such modification was to (i) compare the relative improvements across algorithms, and (ii) compare relative improvements between the background, liver, and lesions of each image.

Results: Analysis of noise-bias curves suggests that NLM improves the reconstructive capabilities of all iterative algorithms considered in the background and liver regions. All algorithms saw a reduction in both bias and noise in the background region: the most significant examples were ART with an average reduction in noise from 43.4% to 27.8% and OSEM with an average reduction in bias from 5.36% to 3.82% throughout their iterations. For liver, all algorithms saw a decrease in noise with a slight increase in bias: the most significant examples were OSEM with an average decrease in noise from 17.68% to 10.26%. For tumor regions, the ART, MLEM, OSEM, SIRT, and TV algorithms all saw reductions in noise, while variations of MLEM and OSEM with penalized linear and quadratic components saw an increase. Figures show reconstructed images using all algorithms without and with NLM, noise-bias trade-off curves for all algorithms, and sample curves comparing standard and NLM adjustments.

Conclusions: For the realistically simulated dataset studied, use of a NLM denoising framework on predicted PET images reconstructed with iterative reconstruction algorithms was shown to improve quantitative performance. While the results are most notable in background and liver regions, improvements in tumor regions are also observed for certain algorithms.

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