# Mixed X-Ray Image Separation for Artworks with Concealed Designs

arXiv: https://arxiv.org/abs/2201.09167 · HTML: https://mlsanity.com/paper/2201.09167/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 23 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Permutation Invariant Training of Deep Models for Speaker-Independent Multi-talker Speech Separation](https://mlsanity.com/paper/1607.00325/) (2016)
- [Single Image Reflection Separation with Perceptual Losses](https://mlsanity.com/paper/1806.05376/) (2018)
- [Learned Convolutional Sparse Coding](https://mlsanity.com/paper/1711.00328/) (2017)
- [Recent Advances in Convolutional Neural Network Acceleration](https://mlsanity.com/paper/1807.08596/) (2018)
- [Neural separation of observed and unobserved distributions](https://mlsanity.com/paper/1811.12739/) (2018)
- [Multi-modal dictionary learning for image separation with application in art investigation](https://mlsanity.com/paper/1607.04147/) (2016)
- [Towards Unsupervised Single-Channel Blind Source Separation using Adversarial Pair Unmix-and-Remix](https://mlsanity.com/paper/1812.07504/) (2018)
- [Parallel proximal methods for total variation minimization](https://mlsanity.com/paper/1510.00466/) (2015)
- [Image Separation with Side Information: A Connected Auto-Encoders Based Approach](https://mlsanity.com/paper/2009.07889/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Lightweight Deep Exclusion Unfolding Network for Single Image Reflection Removal](https://mlsanity.com/paper/2503.01938/) (2025)
- [CLUENet: Cluster Attention Makes Neural Networks Have Eyes](https://mlsanity.com/paper/2512.06345/) (2025)
- [Combined Dictionary Unfolding Network with Gradient-Adaptive Fidelity for Transferable Multi-Source Fusion](https://mlsanity.com/paper/2605.00461/) (2026)
- [MODAL: Multi-Modal Object Re-ID via Model-Driven Sparse Decoupling and Text-Image Differential Filtering](https://mlsanity.com/paper/2608.15096/) (2026)

## Abstract (arXiv)

In this paper, we focus on X-ray images of paintings with concealed sub-surface designs (e.g., deriving from reuse of the painting support or revision of a composition by the artist), which include contributions from both the surface painting and the concealed features. In particular, we propose a self-supervised deep learning-based image separation approach that can be applied to the X-ray images from such paintings to separate them into two hypothetical X-ray images. One of these reconstructed images is related to the X-ray image of the concealed painting, while the second one contains only information related to the X-ray of the visible painting. The proposed separation network consists of two components: the analysis and the synthesis sub-networks. The analysis sub-network is based on learned coupled iterative shrinkage thresholding algorithms (LCISTA) designed using algorithm unrolling techniques, and the synthesis sub-network consists of several linear mappings. The learning algorithm operates in a totally self-supervised fashion without requiring a sample set that contains both the mixed X-ray images and the separated ones. The proposed method is demonstrated on a real painting with concealed content, Do~na Isabel de Porcel by Francisco de Goya, to show its effectiveness.