# NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction

arXiv: https://arxiv.org/abs/2108.10991 · HTML: https://mlsanity.com/paper/2108.10991/

## Key facts

- Cited by 146 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 24 Aug 2021.

## Builds on (most cited first, 13 of 13)

- [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)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [X2CT-GAN: Reconstructing CT from Biplanar X-Rays with Generative Adversarial Networks](https://mlsanity.com/paper/1905.06902/) (2019)
- [DuDoNet: Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/1907.00273/) (2019)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems](https://mlsanity.com/paper/2102.05181/) (2021)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)

## Built on by (most cited first, 30 of 146)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Spatial Functa: Scaling Functa to ImageNet Classification and Generation](https://mlsanity.com/paper/2302.03130/) (2023)
- [Learning Deep Intensity Field for Extremely Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.06681/) (2023)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [A survey of synthetic data augmentation methods in computer vision](https://mlsanity.com/paper/2403.10075/) (2024)
- [Single-subject Multi-contrast MRI Super-resolution via Implicit Neural Representations](https://mlsanity.com/paper/2303.15065/) (2023)
- [Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography](https://mlsanity.com/paper/2209.05483/) (2022)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution](https://mlsanity.com/paper/2303.16242/) (2023)
- [3DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representation](https://mlsanity.com/paper/2312.15676/) (2023)
- [A Survey on Text-guided 3D Visual Grounding: Elements, Recent Advances, and Future Directions](https://mlsanity.com/paper/2406.05785/) (2024)
- [ZeroRF: Fast Sparse View 360deg Reconstruction with Zero Pretraining](https://mlsanity.com/paper/2312.09249/) (2023)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [Medical Image Registration via Neural Fields](https://mlsanity.com/paper/2206.03111/) (2022)
- [Learning 3D Gaussians for Extremely Sparse-View Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2407.01090/) (2024)
- [DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction](https://mlsanity.com/paper/2404.17890/) (2024)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [C^2RV: Cross-Regional and Cross-View Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2406.03902/) (2024)
- [EF-3DGS: Event-Aided Free-Trajectory 3D Gaussian Splatting](https://mlsanity.com/paper/2410.15392/) (2024)
- [Learning Transferable Features for Implicit Neural Representations](https://mlsanity.com/paper/2409.09566/) (2024)
- [Geometry-Aware Attenuation Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.14739/) (2023)
- [Volumetrically Consistent 3D Gaussian Rasterization](https://mlsanity.com/paper/2412.03378/) (2024)
- [Learning Cross-Video Neural Representations for High-Quality Frame Interpolation](https://mlsanity.com/paper/2203.00137/) (2022)
- [Unsupervised Polychromatic Neural Representation for CT Metal Artifact Reduction](https://mlsanity.com/paper/2306.15203/) (2023)
- [Implicit Neural Representations for Robust Joint Sparse-View CT Reconstruction](https://mlsanity.com/paper/2405.02509/) (2024)
- [Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields](https://mlsanity.com/paper/2307.14363/) (2023)
- [CT Reconstruction from Few Planar X-rays with Application towards Low-resource Radiotherapy](https://mlsanity.com/paper/2308.02100/) (2023)

## Abstract (arXiv)

Image reconstruction is an inverse problem that solves for a computational image based on sampled sensor measurement. Sparsely sampled image reconstruction poses addition challenges due to limited measurements. In this work, we propose an implicit Neural Representation learning methodology with Prior embedding (NeRP) to reconstruct a computational image from sparsely sampled measurements. The method differs fundamentally from previous deep learning-based image reconstruction approaches in that NeRP exploits the internal information in an image prior, and the physics of the sparsely sampled measurements to produce a representation of the unknown subject. No large-scale data is required to train the NeRP except for a prior image and sparsely sampled measurements. In addition, we demonstrate that NeRP is a general methodology that generalizes to different imaging modalities such as CT and MRI. We also show that NeRP can robustly capture the subtle yet significant image changes required for assessing tumor progression.