# Neural Fields for NV-Center Inverse Sensing

arXiv: https://arxiv.org/abs/2605.13988 · HTML: https://mlsanity.com/paper/2605.13988/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 85 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 30 of 39)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [AI and the Everything in the Whole Wide World Benchmark](https://mlsanity.com/paper/2111.15366/) (2021)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [The Benchmark Lottery](https://mlsanity.com/paper/2107.07002/) (2021)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020)

## Abstract (arXiv)

Inverse problems in scientific sensing are often solved with either hand-designed regularizers or supervised networks trained on simulated labels, yet both can fail when the forward model is nonlinear, spectrally coupled, and physically delicate. We study this issue for noise sensing based on nitrogen-vacancy (NV) centers in diamond, where a quantum sensor measures magnetic-noise spectra generated by sparse spin sources. We show that replacing a common scalar/coherent forward approximation with a tensor power-summed dipolar operator changes the inverse landscape and exposes a center-collapse failure mode in free-density optimization. We propose NeTMY, an amortization-free coordinate neural field coupled to the differentiable NV forward model, with annealed positional encoding, multiscale optimization, sparsity/gating, and spectrum-fidelity losses. Across sparse synthetic reconstructions generated by the corrected operator, NeTMY achieves the best localization and distributional metrics in the tested benchmark. Mechanism experiments show that NeTMY does not directly execute the raw density-space gradient; its parameterization smooths and redistributes updates, mitigating the center-collapse pathology. These results position NV quantum sensing as a useful testbed for physics-faithful neural inverse problems.