Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction

TL;DR

A novel INR-based Bayesian framework integrating latent variables to capture the common patterns across multiple objects under joint reconstruction of multiple objects using INRs is introduced.

Abstract

Computed Tomography (CT) is pivotal in industrial quality control and medical diagnostics. Sparse-view CT, offering reduced ionizing radiation, faces challenges due to its under-sampled nature, leading to ill-posed reconstruction problems. Recent advancements in Implicit Neural Representations (INRs) have shown promise in addressing sparse-view CT reconstruction. Recognizing that CT often involves scanning similar subjects, we propose a novel approach to improve reconstruction quality through joint reconstruction of multiple objects using INRs. This approach can potentially utilize the advantages of INRs and the common patterns observed across different objects. While current INR joint reconstruction techniques primarily focus on speeding up the learning process, they are not specifically tailored to enhance the final reconstruction quality. To address this gap, we introduce a novel INR-based Bayesian framework integrating latent variables to capture the common patterns across multiple objects under joint reconstruction. The common patterns then assist in the reconstruction of each object via latent variables, thereby improving the individual reconstruction. Extensive experiments demonstrate that our method achieves higher reconstruction quality with sparse views and remains robust to noise in the measurements as indicated by common numerical metrics. The obtained latent variables can also serve as network initialization for the new object and speed up the learning process.

Figures (28)

• Figure 1: Compared to individual reconstruction, joint reconstruction enables INRs to share statistical regularities among multiple objects, thereby enhancing the quality of reconstruction under conditions of sparse-view CT scans and inherent measurement noise. The examples shown here are CT reconstructions of walnuts from a sparse set of projection angles, with the joint reconstruction results obtained using our proposed approach.
• Figure 2: Framework of our proposed method. It uses latent variables to capture the relation among all reconstruction nodes. The latent variables are updated based on all nodes and regularize each individual reconstruction via minimizing the KL divergence terms $D_{KL}$. $\bm{w}_j$ denotes the parameters of j-th node, distributed according to $\mathcal{N}(\bm{\mu}_j,\bm{\rho}_j)$, while $\mathcal{N}(\bm{\omega},\bm{\sigma})$ specifies the prior distribution of parameters $\bm{w}_{1:J}$.
• Figure 3: Visual comparison of reconstruction performance on noiseless measurements. Enlarged areas are highlighted in red insets. PSNR values are on the top left, with SSIM values on the bottom left. Reconstruction of human faces is included to illustrate our method's broad applicability, despite lacking practical relevance in physical contexts. Illustrations figures (first column) are modified from wikimediafigurewalnutwikimediafigurealloywikimediafigurectliu2015deep.
• Figure 4: After the initial 30,000 iterations, each joint reconstruction method undergoes an additional 30,000 iterations for further adaptation.
• Figure 5: The training curve of different methods on noisy measurement. SingleINR, MAML, and FedAvg overfit strongly in 30,000 iterations.