# Compressed Learning: A Deep Neural Network Approach

arXiv: https://arxiv.org/abs/1610.09615 · HTML: https://mlsanity.com/paper/1610.09615/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2016.

## Built on by (most cited first, 8 of 8)

- [TransCL: Transformer Makes Strong and Flexible Compressive Learning](https://mlsanity.com/paper/2207.11972/) (2022)
- [Image-free single-pixel segmentation](https://mlsanity.com/paper/2108.10617/) (2021)
- [Deep Compressed Learning for 3D Seismic Inversion](https://mlsanity.com/paper/2311.00107/) (2023)
- [Remote Multilinear Compressive Learning with Adaptive Compression](https://mlsanity.com/paper/2109.01184/) (2021)
- [Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective](https://mlsanity.com/paper/2105.13191/) (2021)
- [Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery](https://mlsanity.com/paper/2202.03391/) (2022)
- [Accelerated Full Waveform Inversion by Deep Compressed Learning](https://mlsanity.com/paper/2601.01268/) (2026)
- [Learning the Mathematical Property for Designing Low Mutual Coherence Binary Sensing Matrices](https://mlsanity.com/paper/2608.12982/) (2026)

## Abstract (arXiv)

Compressed Learning (CL) is a joint signal processing and machine learning framework for inference from a signal, using a small number of measurements obtained by linear projections of the signal. In this paper we present an end-to-end deep learning approach for CL, in which a network composed of fully-connected layers followed by convolutional layers perform the linear sensing and non-linear inference stages. During the training phase, the sensing matrix and the non-linear inference operator are jointly optimized, and the proposed approach outperforms state-of-the-art for the task of image classification. For example, at a sensing rate of 1% (only 8 measurements of 28 X 28 pixels images), the classification error for the MNIST handwritten digits dataset is 6.46% compared to 41.06% with state-of-the-art.