# Unrolling PALM for sparse semi-blind source separation

arXiv: https://arxiv.org/abs/2112.05694 · HTML: https://mlsanity.com/paper/2112.05694/

## Key facts

- Cited by 3 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 10 Dec 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Learning step sizes for unfolded sparse coding](https://mlsanity.com/paper/1905.11071/) (2019)
- [Nonlinear unmixing of hyperspectral images: models and algorithms](https://mlsanity.com/paper/1304.1875/) (2013)
- [Deep J-Sense: Accelerated MRI Reconstruction via Unrolled Alternating Optimization](https://mlsanity.com/paper/2103.02087/) (2021)
- [Tradeoffs between Convergence Speed and Reconstruction Accuracy in Inverse Problems](https://mlsanity.com/paper/1605.09232/) (2016)
- [Understanding Trainable Sparse Coding via Matrix Factorization](https://mlsanity.com/paper/1609.00285/) (2016)
- [LSALSA: Accelerated Source Separation via Learned Sparse Coding](https://mlsanity.com/paper/1802.06875/) (2018)
- [deep unfolding for non-negative matrix factorization with application to mutational signature analysis](https://mlsanity.com/paper/2108.09138/) (2021)
- [Sparsity and adaptivity for the blind separation of partially correlated sources](https://mlsanity.com/paper/1412.4005/) (2014)

## Built on by (most cited first, 3 of 3)

- [AE-RED: A Hyperspectral Unmixing Framework Powered by Deep Autoencoder and Regularization by Denoising](https://mlsanity.com/paper/2307.00269/) (2023)
- [Super-r'esolution non supervis'ee d'images hyperspectrales de t'el'ed'etection utilisant un entrainement enti`erement synth'etique](https://mlsanity.com/paper/2602.02552/) (2026)
- [Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis](https://mlsanity.com/paper/2607.22262/) (2026)

## Abstract (arXiv)

Sparse Blind Source Separation (BSS) has become a well established tool for a wide range of applications - for instance, in astrophysics and remote sensing. Classical sparse BSS methods, such as the Proximal Alternating Linearized Minimization (PALM) algorithm, nevertheless often suffer from a difficult hyperparameter choice, which undermines their results. To bypass this pitfall, we propose in this work to build on the thriving field of algorithm unfolding/unrolling. Unrolling PALM enables to leverage the data-driven knowledge stemming from realistic simulations or ground-truth data by learning both PALM hyperparameters and variables. In contrast to most existing unrolled algorithms, which assume a fixed known dictionary during the training and testing phases, this article further emphasizes on the ability to deal with variable mixing matrices (a.k.a. dictionaries). The proposed Learned PALM (LPALM) algorithm thus enables to perform semi-blind source separation, which is key to increase the generalization of the learnt model in real-world applications. We illustrate the relevance of LPALM in astrophysical multispectral imaging: the algorithm not only needs up to 104-105 times fewer iterations than PALM, but also improves the separation quality, while avoiding the cumbersome hyperparameter and initialization choice of PALM. We further show that LPALM outperforms other unrolled source separation methods in the semi-blind setting.