# CoCPF: Coordinate-based Continuous Projection Field for Ill-Posed Inverse Problem in Imaging

arXiv: https://arxiv.org/abs/2406.14976 · HTML: https://mlsanity.com/paper/2406.14976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [Deep-neural-network based sinogram synthesis for sparse-view CT image reconstruction](https://mlsanity.com/paper/1803.00694/) (2018)
- [TorchRadon: Fast Differentiable Routines for Computed Tomography](https://mlsanity.com/paper/2009.14788/) (2020)
- [Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography](https://mlsanity.com/paper/2209.05483/) (2022)
- [CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution](https://mlsanity.com/paper/2303.16242/) (2023)
- [Generative Modeling in Sinogram Domain for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2211.13926/) (2022)
- [MetaInv-Net: Meta Inversion Network for Sparse View CT Image Reconstruction](https://mlsanity.com/paper/2006.00171/) (2020)
- [FreeSeed: Frequency-band-aware and Self-guided Network for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2307.05890/) (2023)
- [Sparse-view Cone Beam CT Reconstruction using Data-consistent Supervised and Adversarial Learning from Scarce Training Data](https://mlsanity.com/paper/2201.09318/) (2022)

## Abstract (arXiv)

Sparse-view computed tomography (SVCT) reconstruction aims to acquire CT images based on sparsely-sampled measurements. It allows the subjects exposed to less ionizing radiation, reducing the lifetime risk of developing cancers. Recent researches employ implicit neural representation (INR) techniques to reconstruct CT images from a single SV sinogram. However, due to ill-posedness, these INR-based methods may leave considerable ``holes'' (i.e., unmodeled spaces) in their fields, leading to sub-optimal results. In this paper, we propose the Coordinate-based Continuous Projection Field (CoCPF), which aims to build hole-free representation fields for SVCT reconstruction, achieving better reconstruction quality. Specifically, to fill the holes, CoCPF first employs the stripe-based volume sampling module to broaden the sampling regions of Radon transformation from rays (1D space) to stripes (2D space), which can well cover the internal regions between SV projections. Then, by feeding the sampling regions into the proposed differentiable rendering modules, the holes can be jointly optimized during training, reducing the ill-posed levels. As a result, CoCPF can accurately estimate the internal measurements between SV projections (i.e., DV sinograms), producing high-quality CT images after re-projection. Extensive experiments on simulated and real projection datasets demonstrate that CoCPF outperforms state-of-the-art methods for 2D and 3D SVCT reconstructions under various projection numbers and geometries, yielding fine-grained details and fewer artifacts. Our code will be publicly available.