# SONAR: A Structure-Consistent Neural Operator for Null-Space-Aware Sparse View CT Reconstruction

arXiv: https://arxiv.org/abs/2609.13688 · HTML: https://mlsanity.com/paper/2609.13688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Deep Decomposition Learning for Inverse Imaging Problems](https://mlsanity.com/paper/1911.11028/) (2019)
- [Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions](https://mlsanity.com/paper/2209.13603/) (2022)
- [C^2RV: Cross-Regional and Cross-View Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2406.03902/) (2024)
- [LEARN++: Recurrent Dual-Domain Reconstruction Network for Compressed Sensing CT](https://mlsanity.com/paper/2012.06983/) (2020)
- [Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction](https://mlsanity.com/paper/2405.02509/) (2024)
- [WNet: A data-driven dual-domain denoising model for sparse-view computed tomography with a trainable reconstruction layer](https://mlsanity.com/paper/2207.00400/) (2022)
- [A Unified Model for Compressed Sensing MRI Across Undersampling Patterns](https://mlsanity.com/paper/2410.16290/) (2024)
- [Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2508.10313/) (2025)
- [NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems](https://mlsanity.com/paper/2510.01608/) (2025)
- [Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction](https://mlsanity.com/paper/2404.19075/) (2024)
- [Primal-Dual UNet for Sparse View Cone Beam Computed Tomography Volume Reconstruction](https://mlsanity.com/paper/2205.07866/) (2022)
- [Deep Few-view High-resolution Photon-counting CT at Halved Dose for Extremity Imaging](https://mlsanity.com/paper/2403.12331/) (2024)
- [Cross-Distribution Diffusion Priors-Driven Iterative Reconstruction for Sparse-View CT](https://mlsanity.com/paper/2509.13576/) (2025)
- [Three-dimensional visualization of X-ray micro-CT with large-scale datasets: Efficiency and accuracy for real-time interaction](https://mlsanity.com/paper/2601.15098/) (2026)

## Abstract (arXiv)

Sparse-view computed tomography (CT) reduces radiation dose and acquisition time but remains severely ill-posed because incomplete projections poorly constrain null-space information. Existing learning-based methods often estimate this information in high-dimensional image space, conflate physical measurement errors with prediction errors, and depend on fixed discretizations. We propose SONAR, a Structure-Consistent Neural Operator for Null-Space-Aware Reconstruction. Instead of recovering the full null-space component, SONAR predicts a low-dimensional null-space-aware representation from the acquired projections as pseudo-measurements. It separates measurement and pseudo-measurement residuals, lifts them into the image domain through physics operators, and applies independent neural operators to constrain their structural effects, thereby accommodating admissible errors while suppressing unsupported structures. To support cross-discretization reconstruction, an anisotropic U-shaped neural operator models the periodic angular and nonperiodic detector dimensions using direction-dependent continuous supports, while image-domain neural operators re-discretize continuous kernels on target grids. These components form an optimization-inspired unrolled network. Experiments on simulated AAPM and clinical MARS photon-counting CT data demonstrate consistent improvements across seen and unseen view settings and unseen image resolutions. On AAPM dataset, SONAR improves PSNR by 1.87~dB at 62 views and by 7.63~dB under zero-shot transfer to a 512×512 grid over the strongest competing methods. SONAR also achieves the best overall performance in all clinical settings evaluated, demonstrating accurate, structurally reliable, and discretization-robust sparse-view CT reconstruction.