Penalised Maximum Likelihood Simultaneous Longitudinal PET Image Reconstruction with Difference‐Image Priors

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Abstract

Purpose
Many clinical contexts require the acquisition of multiple positron emission tomography (PET) scans of a single subject, for example to observe and quantify changes in functional behaviour in tumours after treatment in oncology. Typically, the datasets from each of these scans are reconstructed individually, without exploiting the similarities between them. We have recently shown that sharing information between longitudinal PET datasets by penalising voxel‐wise differences during image reconstruction can improve reconstructed images by reducing background noise and increasing the contrast‐to‐noise ratio of high activity lesions. Here we present two additional novel longitudinal difference‐image priors and evaluate their performance using 2D simulation studies and a 3D real dataset case study.

Methods
We have previously proposed a simultaneous difference‐image‐based penalised maximum likelihood (PML) longitudinal image reconstruction method that encourages sparse difference images (DS‐PML), and in this work we propose two further novel prior terms. The priors are designed to encourage longitudinal images with corresponding differences which have i) low entropy (DE‐PML), and ii) high sparsity in their spatial gradients (DTV‐PML). These two new priors and the originally proposed longitudinal prior were applied to 2D simulated treatment response [18F]fluorodeoxyglucose (FDG) brain tumour datasets and compared to standard maximum likelihood expectation‐maximisation (MLEM) reconstructions. These 2D simulation studies explored the effects of penalty strengths, tumour behaviour, and inter‐scan coupling on reconstructed images. Finally, a real two‐scan longitudinal data series acquired from a head and neck cancer patient was reconstructed with the proposed methods and the results compared to standard reconstruction methods.

Results
Using any of the three priors with an appropriate penalty strength produced images with noise levels equivalent to those seen when using standard reconstructions with increased counts levels. In tumour regions each method produces subtly different results in terms of preservation of tumour quantification and reconstruction root mean‐squared error (RMSE). In particular, in the two‐scan simulations, the DE‐PML method produced tumour means in close agreement with MLEM reconstructions, while the DTV‐PML method produced the lowest errors due to noise reduction within the tumour. Across a range of tumour responses and different numbers of scans, similar results were observed, with DTV‐PML producing the lowest errors of the three priors and DE‐PML producing the lowest bias. Similar improvements were observed in the reconstructions of the real longitudinal datasets, although imperfect alignment of the two PET images resulted in additional changes in the difference image that affected the performance of the proposed methods.

Conclusion
Reconstruction of longitudinal datasets by penalising difference images between pairs of scans from a data series allows for noise reduction in all reconstructed images. An appropriate choice of penalty term and penalty strength allows for this noise reduction to be achieved while maintaining reconstruction performance in regions of change, either in terms of quantification of mean intensity via DE‐PML, or in terms of tumour RMSE via DTV‐PML. Overall, improving the image quality of longitudinal datasets via simultaneous reconstruction has the potential to improve upon currently used methods, allow dose reduction, or reduce scan time while maintaining image quality at current levels.
Original languageEnglish
JournalMedical Physics
Early online date26 Apr 2018
Publication statusE-pub ahead of print - 26 Apr 2018

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