Yamac Mehmet, Akpinar Ugur, Sahin Erdem, Kiranyaz Serkan, Gabbouj Moncef
IEEE Trans Image Process. 2023;32:5637-5651. doi: 10.1109/TIP.2023.3318946. Epub 2023 Oct 17.
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 [Formula: see text]. The software implementation of the proposed network is publicly shared at https://github.com/mehmetyamac/GTSNET.
压缩感知（CS）领域的研究工作可分为两类：一是寻找能最大程度保留压缩信息的测量矩阵，二是寻找稳健的重建算法。在传统的CS设置中，测量矩阵被选为随机矩阵，并使用基于优化的迭代解法来恢复信号。在处理大型或多维信号时使用随机矩阵很麻烦，尤其是在进行迭代优化时。最近基于深度学习的解决方案提高了重建精度并加快了恢复速度，但联合学习整个测量矩阵仍然具有挑战性。因此，诸如卷积压缩感知网络（CSNET）等最先进的深度学习CS解决方案采用逐块CS方案来促进学习。在这项工作中，我们通过将测量信号表示为任意数量张量的总和，引入了CS矩阵的可分离多线性学习。与逐块CS相比，张量学习减轻了块状伪影并提高了性能，尤其是在低测量率（MR）下，例如[公式：见原文]。所提出网络的软件实现可在https://github.com/mehmetyamac/GTSNET上公开获取。
