# Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation

arXiv: https://arxiv.org/abs/2108.03167 · HTML: https://mlsanity.com/paper/2108.03167/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 75 references that are in the map.
- First posted on arXiv 4 Aug 2021.

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

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [A Deep Learning Approach to Structured Signal Recovery](https://mlsanity.com/paper/1508.04065/) (2015)
- [MatConvNet - Convolutional Neural Networks for MATLAB](https://mlsanity.com/paper/1412.4564/) (2014)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Convolutional Sparse Support Estimator Network (CSEN) From energy efficient support estimation to learning-aided Compressive Sensing](https://mlsanity.com/paper/2003.00768/) (2020)
- [Multi-level reversible encryption for ECG signals using compressive sensing](https://mlsanity.com/paper/2104.05325/) (2021)
- [Compressively Sensed Image Recognition](https://mlsanity.com/paper/1810.06323/) (2018)
- [Bias Reduction in Compressed Sensing](https://mlsanity.com/paper/1812.11329/) (2018)

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

- [Multiscale Tensor Summation Factorization as a New Neural Network Layer (MTS Layer) for Multidimensional Data Processing](https://mlsanity.com/paper/2504.13975/) (2025)
- [Multi-Scale Tensorial Summation and Dimensional Reduction Guided Neural Network for Edge Detection](https://mlsanity.com/paper/2504.15770/) (2025)
- [A Lightweight Recurrent Learning Network for Sustainable Compressed Sensing](https://mlsanity.com/paper/2304.11674/) (2023)
- [MTS-CSNet: Multiscale Tensor Factorization for Deep Compressive Sensing on RGB Images](https://mlsanity.com/paper/2602.07056/) (2026)

## Abstract (arXiv)

In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the traditional CS setup, the measurement matrices are selected as random matrices, and optimization-based iterative solutions are used to recover the signals. However, when we handle large signals, using random matrices become cumbersome especially when it comes to iterative optimization-based solutions. Even though recent deep learning-based solutions boost the reconstruction accuracy performance while speeding up the recovery, still jointly learning the whole measurement matrix is a difficult process. In this work, we introduce a separable multi-linear learning of the CS matrix by representing it as the summation of arbitrary number of tensors. For a special case where the CS operation is set as a single tensor multiplication, the model is reduced to the learning-based separable CS; while a dense CS matrix can be approximated and learned as the summation of multiple tensors. Both cases can be used in CS of two or multi-dimensional signals e.g., images, multi-spectral images, videos, etc. Structural CS matrices can also be easily approximated and learned in our multi-linear separable learning setup with structural tensor sum representation. Hence, our learnable generalized tensor summation CS operation encapsulates most CS setups including separable CS, non-separable CS (traditional vector-matrix multiplication), structural CS, and CS of the multi-dimensional signals. For both gray-scale and RGB images, the proposed scheme surpasses most state-of-the-art solutions, especially in lower measurement rates. Although the performance gain remains limited from tensor to the sum of tensor representation for gray-scale images, it becomes significant in the RGB case.