RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging

TL;DR

This work tackles dynamic computed tomography under extreme undersampling by addressing the lack of ground-truth dynamic data. It introduces RSR-NF, a framework that represents the dynamic object with a neural field and regularizes it with a pre-trained static restoration prior within the Regularization-by-Denoising (RED) paradigm, solved via an ADMM-based scheme with variable splitting. The key contributions are (i) first integration of neural-field representations with static priors for dynamic reconstructions, (ii) a data-fidelity–temporal-smoothness–RED objective that avoids backpropagation through the restoration network, and (iii) strong empirical gains over baselines such as RED-PSM and TD-DIP on synthetic dCT datasets, including robustness to reduced angular sampling. This approach expands the toolkit for dynamic inverse problems by enabling high-quality reconstructions without dynamic training data, with potential applicability to other dynamic imaging modalities beyond dCT.

Abstract

Dynamic imaging involves the reconstruction of a spatio-temporal object at all times using its undersampled measurements. In particular, in dynamic computed tomography (dCT), only a single projection at one view angle is available at a time, making the inverse problem very challenging. Moreover, ground-truth dynamic data is usually either unavailable or too scarce to be used for supervised learning techniques. To tackle this problem, we propose RSR-NF, which uses a neural field (NF) to represent the dynamic object and, using the Regularization-by-Denoising (RED) framework, incorporates an additional static deep spatial prior into a variational formulation via a learned restoration operator. We use an ADMM-based algorithm with variable splitting to efficiently optimize the variational objective. We compare RSR-NF to three alternatives: NF with only temporal regularization; a recent method combining a partially-separable low-rank representation with RED using a denoiser pretrained on static data; and a deep-image prior-based model. The first comparison demonstrates the reconstruction improvements achieved by combining the NF representation with static restoration priors, whereas the other two demonstrate the improvement over state-of-the art techniques for dCT.

Figures (9)

• Figure 1: The RSR-NF framework. The deep restoration network $D_\phi$ is trained on slices of static objects similar to the object of interest, and the learned spatial prior is used at inference time.
• Figure 2: Ground-truth frames of different dynamic objects. Compressed polymer uniformly sampled in time : full spatio-temporal object for $T$=1001 (top); the second non-overlapping subinterval with $T$=128 (center). Warped walnut for $T=128$ (bottom).
• Figure 3: (a) Representations & corresponding absolute errors for $T$=128 polymer time frames at two times for NF embedding with 7 layers and 64 channels per layer and for a rank-$K$=3 PSM, which has roughly $1.5\times$ more parameters than the NF. (b) Representation PSNR (in dB) for different NF architectures and rank-$K$ PSM.
• Figure 4: Reconstruction PSNR vs. $t$ for (i) walnut and (ii) polymer. The shaded area for TD-DIP shows the interval between the best and the worst PSNR in three runs with random initialization.
• Figure 5: Reconstruction PSNR vs. number of distinct view angles $\hat{P}$ with $P=128$ for (i) walnut, and (ii) polymer subinterval.