2021/08/04 by Mehmet Yamaç, Mehmet Yamac, Ugur Akpinar +10 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Data Compression Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Indoor and Outdoor Localization Technologies #Information Theory (cs.IT) #Machine Learning (cs.LG) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #cs.IT #cs.LG #eess.SP #electronic engineering #information engineering #math.IT
paper · pdf · doi:10.48550/arxiv.2108.03167
The software implementation of the proposed network is publicly shared at https://github.com/mehmetyamac/GTSNET
arxiv created 2021/08/04 · openalex publication_date 2021/08/04 · arxiv updated 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.