AR3D-R1: Advances in 3D Imaging

• AR3D-R1 is a framework that unifies unsupervised ring-artifact reduction in CBCT, RED-based array SAR imaging, and neural relightable 3D reconstruction.
• It leverages principled inverse problem formulations and data-driven regularizers to achieve high fidelity metrics like PSNR and SSIM across various domains.
• The practical applications span medical imaging, remote sensing, and computer graphics, demonstrating robust performance under sparse and noisy conditions.

AR3D-R1 refers to state-of-the-art approaches in three distinct domains: (1) unsupervised ring-artifact reduction in 3D X-ray CBCT, (2) array SAR 3D sparse imaging based on Regularization by Denoising (RED), and (3) neural relightable 3D appearance reconstruction. Each instantiation of AR3D-R1 addresses critical challenges in high-dimensional imaging via principled inverse problem formulations and data-driven regularization methodologies. The following sections synthesize the technical foundations, algorithms, performance characteristics, and limitations across these recent works (Wu et al., 8 Dec 2024, Wang et al., 9 May 2024, Feng et al., 16 Nov 2024).

1. Multi-Parameter Inverse Problem in 3D X-ray CBCT

AR3D-R1, also termed "Riner", reframes ring artifact reduction in 3D cone-beam CT as a multi-parameter inverse problem centered on the physical model of detector response nonidealities. Measurements are described by the discretized Lambert–Beer law,

$$I(\theta,s) = \alpha_s I_0 \exp\left(-\int_{L(\theta,s)} \mu(x)\,dx\right),$$

where $\mu(x)$ is the clean attenuation field and $\alpha_s$ the per-detector response. The forward model incorporates both valid and defective detectors using a binary mask $m(s)$, yielding a sinogram entry,

$$\rho(\theta,s) = \left[-\ln(\max(\alpha_s,0)+\epsilon_{\text{const}}) + \sum_{x\in L(\theta,s)} \mu(x)\,\Delta x \right] \cdot m(s).$$

The inverse objective jointly estimates the implicit neural field $\mu(x)$ (an MLP encoded via Instant-NGP hash grids) and $\alpha = [\alpha_1, \dots, \alpha_S]$ by minimizing

$$L(\Phi,\alpha) = \sum_{\theta\in\Theta} \sum_{s\in S_{\text{sub}}} \left\|\rho(\theta, s) - \hat\rho(\theta, s;\Phi, \alpha) \right\|_1,$$

without explicit regularization, relying instead on the spectral bias of neural fields. Mini-batch ray-based optimization scales linearly with the number of rays and samples, facilitating memory-efficient joint inference over large 3D volumes with no external training data (Wu et al., 8 Dec 2024).

2. Regularization by Denoising in 3D Array SAR Imaging

AR3D-R1 also designates an array SAR 3D sparse imaging framework leveraging RED, which substitutes traditional handcrafted priors with explicit state-of-the-art denoising operators. The SAR forward model is

$y = A x + n,$

where $A$ is the measurement operator encapsulating spatial phase delays. The RED cost function is

$$J(x) = \frac{1}{2} \|Ax - y\|_2^2 + \frac{\lambda}{2} x^T(x - D(x)),$$

with $D(\cdot)$ a denoiser such as NLM, BM3D, DnCNN, or IRCNN. Two proximal-gradient-type solvers are employed:

• RED-ADMM (RADMM): Alternately updates $x$ via linear solves and $v$ via denoising-based fixed-point iterations, with dual variable updates for convergence.
• RED-GAP (RGAP): Applies explicit data-consistency projections and view-pooling.

Under conditions where $D$ is cyclically-nonexpansive, theoretical guarantees ensure convexity and convergence. Experimental benchmarks demonstrate superior quantitative fidelity (e.g., $48.2$ dB PSNR, $0.976$ SSIM at $50\%$ sampling rate) and robustness to severe undersampling and noise, outperforming non-learning and plug-and-play baselines (Wang et al., 9 May 2024).

3. Neural Relightable 3D Appearance Reconstruction

In the context of sparse-view 3D appearance reconstruction, AR3D-R1 architectures enable explicit decoupling of geometry and appearance to solve for relightable, physically-based rendering (PBR) maps over UV space. The ARM pipeline comprises:

• GeoRM: Transformer-triplane feature extraction and MLP density decoding for geometry, followed by differentiable Marching Cubes mesh extraction.
• GlossyRM: Predicts per-vertex roughness and metalness on fixed meshes.
• InstantAlbedo: Fuses six back-projected measurement UV maps via U-Net and FFC (Fast Fourier Convolution) modules, outputting both baked-lighting color and diffuse albedo.

Disentanglement of illumination vs. material properties is achieved by integrating a material-aware encoder (DINO ViT, pretrained on segmentation datasets), which is back-projected into UV space alongside raw colors to inform the network. Optimization exploits multi-scale semantic cues to suppress baked-in highlights and enhance robustness under sparse observations (Feng et al., 16 Nov 2024).

4. Experimental Evaluation and Key Performance Metrics

Rigorous empirical comparisons substantiate the efficacy of AR3D-R1 methodologies:

• In ring-artifact reduction, AR3D-R1 achieves $38.93$ dB PSNR and $0.965$ SSIM on DeepLesion test slices, surpassing both supervised and unsupervised SOTA baselines (Wu et al., 8 Dec 2024).
• For array SAR imaging, RED-based approaches yield up to $+4$ dB PSNR improvement over matched filter or convex priors, with stable artifact suppression at extreme undersampling (SR $= 15\%$) and low SNR (Wang et al., 9 May 2024).
• For relightable 3D reconstruction, ARM achieves $0.968$ F-Score, $0.049$ Chamfer Distance, $21.69$ dB PSNR, and $0.880$ SSIM—outperforming MeshFormer and others. Relighted images maintain $21.750$ dB PSNR-A and $0.171$ LPIPS-A (Feng et al., 16 Nov 2024).

A table summarizing core metrics across domains:

Domain	Key Metric	AR3D-R1 Performance
3D X-ray CBCT (RAR)	PSNR [dB], SSIM	38.93, 0.965
Array SAR 3D Imaging	PSNR [dB], SSIM	48.2, 0.976
Relightable 3D Gen.	F-Score, PSNR, SSIM	0.968, 21.69, 0.880

5. Scalability, Generalization, and Algorithmic Limitations

AR3D-R1 frameworks are designed with scalability and generalization in mind:

• CBCT RAR generalizes across both fan-beam and cone-beam geometries and diverse detector types without paired training data, leveraging the spectral bias of neural implicit fields to regularize ill-posedness (Wu et al., 8 Dec 2024).
• Array SAR RED imaging is robust to high-dimensional data, few observations, and noise due to adaptive denoising priors and operator-splitting solvers with provable convergence (Wang et al., 9 May 2024).
• ARM-based 3D appearance reconstruction isolates geometry and appearance learning, but faces potential inconsistencies in upstream multi-view synthesis and discrete atlas unwrapping artifacts (Feng et al., 16 Nov 2024).

Remaining challenges include per-case optimization overhead (e.g., $\sim15$ min/volume for CBCT), lack of explicit regularizers for detector responses, opportunities for algorithmic acceleration (e.g., K-planes, splatting), and material segmentation reliability.

6. Future Directions and Research Opportunities

Emergent AR3D-R1 methods prompt several research avenues:

• For ring artifact reduction: integrating explicit regularizers on detector responses, jointly modeling measurement noise, and extending inverse solvers to time-varying or spectral CT.
• For array SAR imaging: designing adaptive denoiser selection strategies, exploring deeper CNN models, and optimizing penalty parameters for convergence speed vs. reconstruction fidelity.
• For relightable 3D reconstruction: joint refinement of unwrapping and texture inference, learnable view aggregation for conflict resolution, and incorporation of real multi-illumination datasets for enhanced priors.

A plausible implication is that the multi-parameter inverse problem paradigm, when integrated with neural representations and explicit denoising-based regularizers, can generalize to other volumetric, imaging, or inverse rendering tasks in scientific and industrial domains.