In this work, we propose a novel approach called Operational Support Estimator Networks (OSENs) for the support estimation task. Support Estimation (SE) is defined as finding the locations of non-zero elements in a sparse signal. By its very nature, the mapping between the measurement and sparse signal is a non-linear operation. Traditional support estimators rely on computationally expensive iterative signal recovery techniques to achieve such non-linearity. Contrary to the convolution layers, the proposed OSEN approach consists of operational layers that can learn such complex non-linearities without the need for deep networks. In this way, the performance of the non-iterative support estimation is greatly improved. Moreover, the operational layers comprise so-called generative \textit{super neurons} with non-local kernels. The kernel location for each neuron/feature map is optimized jointly for the SE task during the training. We evaluate the OSENs in three different applications: i. support estimation from Compressive Sensing (CS) measurements, ii. representation-based classification, and iii. learning-aided CS reconstruction where the output of OSENs is used as prior knowledge to the CS algorithm for an enhanced reconstruction. Experimental results show that the proposed approach achieves computational efficiency and outperforms competing methods, especially at low measurement rates by a significant margin. The software implementation is publicly shared at https://github.com/meteahishali/OSEN.

翻译：在本文中，我们提出了一种称为操作支持估计网络（OSENs）的新方法，用于支持估计任务。支持估计定义为寻找稀疏信号中非零元素的位置。本质上，测量信号与稀疏信号之间的映射是一种非线性操作。传统支持估计器依赖计算成本高的迭代信号恢复技术来实现这种非线性。与卷积层不同，所提出的OSEN方法包含能够学习此类复杂非线性而无需深层网络的操作层。通过这种方式，非迭代支持估计的性能得到了显著提升。此外，这些操作层由具有非局部核的生成性超级神经元组成。每个神经元/特征图的核位置在训练过程中针对支持估计任务进行联合优化。我们在三种不同应用中评估了OSENs：i. 从压缩感知（CS）测量中进行支持估计，ii. 基于表示的分类，以及iii. 学习辅助的CS重建，其中OSENs的输出作为先验知识用于CS算法以实现增强重建。实验结果表明，所提出的方法实现了计算效率，并在性能上优于竞争方法，尤其是在低测量率条件下表现显著优越。软件实现已公开分享于https://github.com/meteahishali/OSEN。