Operational Support Estimator Networks

TL;DR

Experimental results show that the proposed OSEN approach achieves computational efficiency and outperforms competing methods, especially at low measurement rates by significant margins.

Abstract

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.

Figures (8)

• Figure 1: The proposed OSEN approach with non-localized and non-linear kernels for the SE task. For a sparse image/signal $\mathbf{x}$ in spatial domain ($\mathbf{\Phi} = \mathbf{I}$), rough and noisy estimation is first performed by $\widetilde{\mathbf{x}}=\mathbf{B}\mathbf{y}$ where $\mathbf{y}$ is the measurement. Support locations corresponding to non-zero elements are then found in the form of segmentation masks.
• Figure 2: The proposed OSEN approach with non-localized and non-linear kernels for the representation-based classification task. The representative dictionary $\mathbf{D}$ is formed by applying a dimensionality reduction with matrix $\mathbf{A}$ to stacked dictionary samples ($\mathbf{\Phi}$). For a vectorized query image $\mathbf{y}$, rough and noisy estimation for support locations is performed by $\widetilde{\mathbf{x}}=\mathbf{B}\mathbf{y}$. Then, support locations are computed to estimate the class label.
• Figure 3: The proposed NCL-OSEN approach has a proxy mapping layer equipped with Self-GOPs as defined in \ref{['eq:perceptron']}. The network is trained end-to-end and the proxy mapping layer is jointly optimized with the support estimation and classification parts.
• Figure 4: Obtained $F_1$-Scores by the methods under noisy measurements using different Measurement Rates (MRs).
• Figure 5: Classification accuracy versus computational time for the proposed OSEN and competing approaches. CSEN$+$ has two times more neurons in the hidden layers.