# Adaptive Graph-based Total Variation for Tomographic Reconstructions

arXiv: https://arxiv.org/abs/1610.00893 · HTML: https://mlsanity.com/paper/1610.00893/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2016.

## Built on by (most cited first, 6 of 6)

- [DuDoTrans: Dual-Domain Transformer Provides More Attention for Sinogram Restoration in Sparse-View CT Reconstruction](https://mlsanity.com/paper/2111.10790/) (2021)
- [Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation](https://mlsanity.com/paper/2103.05255/) (2021)
- [Robust Graph Representation Learning for Local Corruption Recovery](https://mlsanity.com/paper/2202.04936/) (2022)
- [Active CT Reconstruction with a Learned Sampling Policy](https://mlsanity.com/paper/2211.01670/) (2022)
- [Compressive Recovery of Signals Defined on Perturbed Graphs](https://mlsanity.com/paper/2402.07637/) (2024)
- [Deep Inertia Lp Half-Quadratic Splitting Unrolling Network for Sparse View CT Reconstruction](https://mlsanity.com/paper/2408.06600/) (2024)

## Abstract (arXiv)

Sparsity exploiting image reconstruction (SER) methods have been extensively used with Total Variation (TV) regularization for tomographic reconstructions. Local TV methods fail to preserve texture details and often create additional artefacts due to over-smoothing. Non-Local TV (NLTV) methods have been proposed as a solution to this but they either lack continuous updates due to computational constraints or limit the locality to a small region. In this paper, we propose Adaptive Graph-based TV (AGTV). The proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the entire image regardless of spatial distance. As compared to NLTV the proposed method is computationally efficient and involves updating the graph prior during every iteration making the connection between similar regions stronger. Moreover, it promotes sparsity in the wavelet and graph gradient domains. Since TV is a special case of graph TV the proposed method can also be seen as a generalization of SER and TV methods.