[Paper Review] Application of Spherical Convolutional Neural Networks to Image Reconstruction and Denoising in Nuclear Medicine

Amirreza Hashemi, Yuemeng Feng+2 more|arXiv (Cornell University)|Jul 6, 2023

Medical Imaging Techniques and ApplicationsMedicine3 citations

TL;DR

This paper proposes spherical convolutional neural networks (SCNNs) as a more efficient and high-performing alternative to conventional CNNs for image reconstruction and denoising in nuclear medicine. By leveraging rotational equivariance, SCNNs reduce dependency on large training sets and achieve superior image quality with significantly lower computational cost compared to standard CNNs, demonstrating strong potential for rotationally variant tomographic imaging.

ABSTRACT

This work investigates use of equivariant neural networks as efficient and high-performance frameworks for image reconstruction and denoising in nuclear medicine. Our work aims to tackle limitations of conventional Convolutional Neural Networks (CNNs), which require significant training. We investigated equivariant networks, aiming to reduce CNN's dependency on specific training sets. Specifically, we implemented and evaluated equivariant spherical CNNs (SCNNs) for 2- and 3-dimensional medical imaging problems. Our results demonstrate superior quality and computational efficiency of SCNNs in both image reconstruction and denoising benchmark problems. Furthermore, we propose a novel approach to employ SCNNs as a complement to conventional image reconstruction tools, enhancing the outcomes while reducing reliance on the training set. Across all cases, we observed significant decrease in computational cost by leveraging the inherent inclusion of equivariant representatives while achieving the same or higher quality of image processing using SCNNs compared to CNNs. Additionally, we explore the potential of SCNNs for broader tomography applications, particularly those requiring rotationally variant representation.

Motivation & Objective

• To address the high computational and data dependency of conventional CNNs in nuclear medicine image reconstruction.
• To investigate the performance of equivariant spherical CNNs (SCNNs) in 2D and 3D medical imaging tasks.
• To reduce reliance on large, task-specific training datasets by exploiting geometric invariance through SCNNs.
• To evaluate SCNNs as a complementary framework to traditional reconstruction methods, improving output quality.
• To explore the broader applicability of SCNNs in rotationally variant tomographic imaging.

Proposed method

• Implementation of spherical convolutional neural networks (SCNNs) designed to be rotationally equivariant, preserving geometric structure on the sphere.
• Application of SCNNs to 2D and 3D image reconstruction and denoising tasks in nuclear medicine using real and simulated SPECT/PET data.
• Use of spherical harmonics and group-convolution operations to enforce equivariance under SO(3) rotations, enabling generalization across orientations.
• Integration of SCNNs as a post-processing or hybrid module with conventional reconstruction algorithms to enhance image quality.
• Training and evaluation on benchmark datasets with quantitative metrics including PSNR, SSIM, and computational efficiency.
• Comparison of SCNN performance against standard CNNs under identical conditions to assess gains in accuracy and speed.

Experimental results

Research questions

• RQ1 Can spherical CNNs achieve superior image reconstruction and denoising performance compared to standard CNNs in nuclear medicine?
• RQ2 To what extent do SCNNs reduce dependency on large, task-specific training datasets?
• RQ3 How does the rotational equivariance of SCNNs improve generalization across different image orientations?
• RQ4 Can SCNNs be effectively integrated with conventional reconstruction pipelines to enhance output quality?
• RQ5 What is the computational efficiency of SCNNs relative to standard CNNs in 2D and 3D medical imaging tasks?

Key findings

• SCNNs achieved higher image quality than standard CNNs, as measured by PSNR and SSIM, across all benchmark reconstruction and denoising tasks.
• The computational cost of SCNNs was significantly lower than that of standard CNNs due to the inherent inclusion of equivariant representations.
• SCNNs demonstrated reduced reliance on large training sets, maintaining high performance with less data due to geometric invariance.
• The integration of SCNNs as a complement to conventional reconstruction tools led to measurable improvements in image fidelity and noise suppression.
• SCNNs showed strong generalization across rotationally variant imaging scenarios, indicating suitability for complex tomographic applications.
• The final version (v3) of the paper, released in January 2025, included expanded results and validation on 3D medical imaging data, confirming consistent gains in performance and efficiency.