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

Research output: Contribution to journalArticleScientificpeer-review


The efforts in compressive sensing (CS) literature can be divided into two groups: finding a measurement matrix that preserves the compressed information at its maximum level, and finding a robust reconstruction algorithm. In the traditional CS setup, the measurement matrices are selected as random matrices, and optimization-based iterative solutions are used to recover the signals. Using random matrices when handling large or multi-dimensional signals is cumbersome especially when it comes to iterative optimizations. Recent deep learning-based solutions increase reconstruction accuracy while speeding up recovery, but jointly learning the whole measurement matrix remains challenging. For this reason, state-of-the-art deep learning CS solutions such as convolutional compressive sensing network (CSNET) use block-wise CS schemes to facilitate learning. In this work, we introduce a separable multi-linear learning of the CS matrix by representing the measurement signal as the summation of the arbitrary number of tensors. As compared to block-wise CS, tensorial learning eases blocking artifacts and improves performance, especially at low measurement rates (MRs), such as {MRs} < 0.1. The software implementation of the proposed network is publicly shared at

Original languageEnglish
Pages (from-to)5637-5651
Number of pages15
JournalIEEE Transactions on Image Processing
Publication statusPublished - 2023
Publication typeA1 Journal article-refereed


  • Compressive sensing
  • deep reconstruction
  • separable compressive learning
  • tensorial compressive learning

Publication forum classification

  • Publication forum level 3

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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