  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.
