Implicit neural representations for end-to-end PET reconstruction

TL;DR

This work addresses end-to-end PET reconstruction from sinograms using implicit neural representations (INRs) with the SIREN architecture. It proposes an unsupervised framework that represents the image as a continuous function $\lambda = f_N(\theta|v)$ and optimizes it jointly with a forward projection model under a Poisson likelihood, without requiring large training datasets. Compared to BSREM and DIP baselines on BrainWeb-inspired phantom data with realistic sinograms, the SIREN-based method achieves higher PET-specific metrics, notably improved activity recovery and contrast, while reducing image roughness and converging faster. The approach demonstrates the potential of INRs for high-fidelity PET reconstruction and motivates extensions to 3D real data and automatic hyperparameter tuning.

Abstract

Implicit neural representations (INRs) have demonstrated strong capabilities in various medical imaging tasks, such as denoising, registration, and segmentation, by representing images as continuous functions, allowing complex details to be captured. For image reconstruction problems, INRs can also reduce artifacts typically introduced by conventional reconstruction algorithms. However, to the best of our knowledge, INRs have not been studied in the context of PET reconstruction. In this paper, we propose an unsupervised PET image reconstruction method based on the implicit SIREN neural network architecture using sinusoidal activation functions. Our method incorporates a forward projection model and a loss function adapted to perform PET image reconstruction directly from sinograms, without the need for large training datasets. The performance of the proposed approach was compared with that of conventional penalized likelihood methods and deep image prior (DIP) based reconstruction using brain phantom data and realistically simulated sinograms. The results show that the INR-based approach can reconstruct high-quality images with a simpler, more efficient model, offering improvements in PET image reconstruction, particularly in terms of contrast, activity recovery, and relative bias.

Figures (3)

• Figure 1: Overview of the proposed pipeline for PET reconstruction using SIREN. The model maps the image pixel by pixel to construct the full image. The loss is then computed in the measurement domain between the estimated sinogram obtained by projecting the estimated image and the measured sinogram.
• Figure 2: Image Roughness (IR) versus Activity Recovery and Relative Bias, plotted for each iteration for SIREN and DIP, and for different regularization strength in the case of BSREM with quadratic penalty.
• Figure 3: Reconstructed images using BSREM with quadratic penalty, DIP and SIREN.