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 sparse signals. 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 convolutional 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 non-iterative support estimation is greatly improved. Moreover, the operational layers comprise so-called generative super neurons with non-local kernels. The kernel location for each neuron/feature map is optimized jointly for the SE task during 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 enhanced reconstruction. Experimental results show that the proposed approach achieves computational efficiency and outperforms competing methods, especially at low measurement rates by significant margins. The software implementation is shared at https://github.com/meteahishali/OSEN.

翻译：本文提出了一种名为操作支持估计器网络（OSENs）的新方法，用于支持估计任务。支持估计（SE）定义为寻找稀疏信号中非零元素的位置。就其本质而言，测量值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昂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方法包含操作层，无需深层网络即可学习这种复杂的非线性特性，从而显著提升了非迭代支持估计的性能。此外，操作层由具有非局部核的所谓生成超神经元组成。在训练过程中，每个神经元/特征图的核位置针对SE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）测量值中估计支持，ii. 基于表示的分类，以及iii. 学习辅助的CS重构，其中OSENs的输出作为先验知识用于CS算法以增强重构效果。实验结果表明，所提方法在计算效率上具有优势，尤其在低测量率下以显著优势优于竞争方法。软件实现代码已共享于 https://github.com/meteahishali/OSEN。