# Distributed Compressive Sensing: A Deep Learning Approach

arXiv: https://arxiv.org/abs/1508.04924 · HTML: https://mlsanity.com/paper/1508.04924/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2015.

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

- [JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging](https://mlsanity.com/paper/2205.07770/) (2022)
- [Deep Learning-based Compressive Beam Alignment in mmWave Vehicular Systems](https://mlsanity.com/paper/2103.00125/) (2021)
- [Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective](https://mlsanity.com/paper/2105.13191/) (2021)
- [Joint User and Data Detection in Grant-Free NOMA with Attention-based BiLSTM Network](https://mlsanity.com/paper/2209.06392/) (2022)
- [Exploring the Power of Generative Deep Learning for Image-to-Image Translation and MRI Reconstruction: A Cross-Domain Review](https://mlsanity.com/paper/2303.09012/) (2023)
- [Compressed Sensor Caching and Collaborative Sparse Data Recovery with Anchor Alignment](https://mlsanity.com/paper/2406.10137/) (2024)

## Abstract (arXiv)

Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this condition. Instead we assume that these sparse vectors depend on each other but that this dependency is unknown. We capture this dependency by computing the conditional probability of each entry in each vector being non-zero, given the "residuals" of all previous vectors. To estimate these probabilities, we propose the use of the Long Short-Term Memory (LSTM)[1], a data driven model for sequence modelling that is deep in time. To calculate the model parameters, we minimize a cross entropy cost function. To reconstruct the sparse vectors at the decoder, we propose a greedy solver that uses the above model to estimate the conditional probabilities. By performing extensive experiments on two real world datasets, we show that the proposed method significantly outperforms the general MMV solver (the Simultaneous Orthogonal Matching Pursuit (SOMP)) and a number of the model-based Bayesian methods. The proposed method does not add any complexity to the general compressive sensing encoder. The trained model is used just at the decoder. As the proposed method is a data driven method, it is only applicable when training data is available. In many applications however, training data is indeed available, e.g. in recorded images and videos.