E-Optimal Sensor Selection for Compressive Sensing-Based Purposes

Collaborative estimation of a sparse vector $\mathbf {x}$x by $M$M potential measurements is considered. Each measurement is the projection of $\mathbf {x}$x obtained by a regressor, i.e., $y_m=\mathbf {a}_m^T \mathbf {x}$ym=amTx . The problem of selecting $K$K sensor measurements from a set of $M$M potential sensors is studied where $K\ll M$K≪M and $K$K is less than the dimension of $\mathbf {x}$x . In other words, we aim to reduce the problem to an under-determined system of equations in which a sparse solution is desired. This paper suggests selecting sensors in a way that the reduced matrix construct a well conditioned measurement matrix. Our criterion is based on E-optimality, which is highly related to the restricted isometry property that provides some guarantees for sparse solution obtained by $\ell _1$ℓ1 minimization. The proposed basic E-optimal selection is vulnerable to outlier and noisy data. The robust version of the algorithm is presented for distributed selection for big data sets. Moreover, an online implementation is proposed that involves partially observed measurements in a sequential manner. Our simulation results show the proposed method outperforms the other criteria for collaborative spectrum sensing in cognitive radio networks (CRNs). Our suggested selection method is evaluated in machine learning applications. It is used to pick up the most informative features/data. Specifically, the proposed method is exploited for face recognition with partial training data.