# Unrolled Compressed Blind-Deconvolution

arXiv: https://arxiv.org/abs/2209.14165 · HTML: https://mlsanity.com/paper/2209.14165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 28 Sep 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [Learning to Invert: Signal Recovery via Deep Convolutional Networks](https://mlsanity.com/paper/1701.03891/) (2017)
- [Stable and Interpretable Unrolled Dictionary Learning](https://mlsanity.com/paper/2106.00058/) (2021)
- [DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural Networks](https://mlsanity.com/paper/1707.03386/) (2017)
- [Scalable Convolutional Dictionary Learning with Constrained Recurrent Sparse Auto-encoders](https://mlsanity.com/paper/1807.04734/) (2018)
- [Unfolding Neural Networks for Compressive Multichannel Blind Deconvolution](https://mlsanity.com/paper/2010.11391/) (2020)
- [RandNet: deep learning with compressed measurements of images](https://mlsanity.com/paper/1908.09258/) (2019)
- [Blind Gain and Phase Calibration via Sparse Spectral Methods](https://mlsanity.com/paper/1712.00111/) (2017)
- [Identifiability Conditions for Compressive Multichannel Blind Deconvolution](https://mlsanity.com/paper/2001.00613/) (2020)

## Built on by (most cited first, 2 of 2)

- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Tunable Domain Adaptation Using Unfolding](https://mlsanity.com/paper/2603.26931/) (2026)

## Abstract (arXiv)

The problem of sparse multichannel blind deconvolution (S-MBD) arises frequently in many engineering applications such as radar/sonar/ultrasound imaging. To reduce its computational and implementation cost, we propose a compression method that enables blind recovery from much fewer measurements with respect to the full received signal in time. The proposed compression measures the signal through a filter followed by a subsampling, allowing for a significant reduction in implementation cost. We derive theoretical guarantees for the identifiability and recovery of a sparse filter from compressed measurements. Our results allow for the design of a wide class of compression filters. We, then, propose a data-driven unrolled learning framework to learn the compression filter and solve the S-MBD problem. The encoder is a recurrent inference network that maps compressed measurements into an estimate of sparse filters. We demonstrate that our unrolled learning method is more robust to choices of source shapes and has better recovery performance compared to optimization-based methods. Finally, in data-limited applications (fewshot learning), we highlight the superior generalization capability of unrolled learning compared to conventional deep learning.