Dual-Input Dynamic Convolution for Positron Range Correction in PET Image Reconstruction

TL;DR

This work tackles the challenge of positron range blurring in PET, especially for high-energy emitters like Ga-68, by introducing DDConv, a CNN-based method that predicts voxel-specific PR PSFs from local attenuation and a distance cue. DDConv integrates both forward PR blurring and its transpose into the iterative reconstruction framework, ensuring mathematical consistency with the EM algorithm while achieving near Monte Carlo accuracy at a fraction of the computational cost. Across digital phantoms, XCAT simulations, and real phantom data, DDConv outperforms the state-of-the-art SVTD method, particularly at tissue interfaces such as lung–soft tissue and bone–soft tissue, and demonstrates robust activity recovery in heterogeneous regions. The approach enables practical, physically faithful PR correction for routine PET imaging, with open-source code and accelerations to further support clinical adoption and future extensions to diverse tracers and scanner geometries.

Abstract

Positron range (PR) blurring degrades positron emission tomography (PET) image resolution, particularly for high-energy emitters like gallium-68 (68 Ga). We introduce Dual-Input Dynamic Convolution (DDConv), a novel computationally efficient approach trained with voxel-specific PR point spread functions (PSFs) from Monte Carlo (MC) simulations and designed to be utilized within an iterative reconstruction algorithm to perform PR correction (PRC). By dynamically inferring local blurring kernels through a trained convolutional neural network (CNN), DDConv captures complex tissue interfaces more accurately than prior methods. Additionally, it also computes the transpose operator, ensuring consistency within iterative PET reconstruction. Comparisons with a state-of-the-art, tissue-dependent correction confirm the advantages of DDConv in recovering higher-resolution details in heterogeneous regions, including bone-soft tissue and lung-soft tissue boundaries. Experiments across digital phantoms and MC-simulated data show that DDConv offers near-MC accuracy and outperforms the state-of-the-art technique, namely spatially-variant and tissue-dependent (SVTD), especially in areas with complex material interfaces. Results from real phantom experiments further confirm DD-Conv's robustness and practical applicability: while both DD-Conv and SVTD performed similarly in homogeneous soft-tissue regions, DDConv provided more accurate activity recovery and sharper delineation at heterogeneous lung-soft tissue interfaces. Our code available at https://github.com/mellak/ddconv-prc.

Figures (10)

• Figure 1: Random material images $\bm{\eta}$ (upper row) with tissue-specific color coding---pink for lung, light blue for water, and gray for bone---and their corresponding MC-generated PR PSF $\bm{w}_{\bm{\eta}}$ (annihilation image). The yellow spot represents the Ga68 positron-emitting point source. We used a 11×11×11 window with 2-mm cubic voxels
• Figure 2: Illustration of the PR blurring operators. The top section represents the transposed operator $\bm{B}(\bm{\mu})^\top$, while the bottom section shows the forward operator $\bm{B}(\bm{\mu})$. Both operations use spatially varying PSFs $\bm{w}_j$ predicted by the same model $\bm{G}_{\bm{\theta}}$, based on the local attenuation image $\bm{\mu}_{\mathcal{N}_j}$. The right side details the architecture of $\bm{G}_{\bm{\theta}}$.
• Figure 3: Experiment 1---Digital phantoms used to assess PR blurring accuracy (pink for lung, light blue for water).
• Figure 4: Experiment 1---Overview of PR distributions across different viewing axes with the digital phantoms from Figure \ref{['fig:phantoms']} (pink for lung, light blue for water) with MC simulations (reference), SVTD and DDConv.
• Figure 5: Experiment 1---PR blurring experiment with the XCAT phantom: \ref{['subfig:xcat_act']} activity phantom, \ref{['subfig:xcat_mat']} material phantom, \ref{['subfig:xcat_mc']} annihilation image (MC simulation), \ref{['subfig:xcat_svtd']}SVTD-blurred activity, \ref{['subfig:xcat_ddconv']}DDConv-blurred activity and \ref{['subfig:xcat_profiles']} profiles across the green line.