# Bayesian Compressive Sensing Based Optimized Node Selection Scheme in Underwater Sensor Networks
## 1 Introduction
### Related Works and Motivation  
Compressed sensing, which has been studied by many scholars [12; 13; 14; 15], is a vital technique for decreasing the samples in the information acquisition. For example, the authors in [16] applied a compressed sensing method to multipath channel estimation. In [17], the authors designed an optimized compressed sensing matrix and applied it to the sparse channel estimation. In [18], the directions of arrival estimation were studied by a compressed sensing method and it is robust and very accurate. Compressed sensing theory is also used to develop the practical incoherent undersampling schemes for rapid MR imaging [19]. By using a compressed sensing method, a semi-analytic scheme is developed to solve the iterative clipping noise recovery in [20]. By taking advantage of the compressed sensing method, the authors in [21] addressed nonlinear inverse scattering problems. Furthermore, examples with experimental data also showed the effectiveness of the compressed sensing method in position and shape reconstruction [22]. In addition, compressed sensing theory can be used to cancer imaging about the induced magnetic anomaly [23]. Therefore, it is it is of significance to develop the application of the compressed sensing technique. In recent years, Bayesian compressive sensing has been widely investigated due to its advantages of giving posterior density function and error covariance matrix. For instance, a Bayesian compressive sensing method is used to estimate complex-valued targets in wireless localization systems [24]. Thermal imaging is studied with an application of Bayesian compressive sensing in [25]. In [26], the authors provided an estimation for direction of arrival based on Bayesian compressive sensing and gave a Kalman filter to analyze the signals. A Bayesian compressive sensing framework was used to develop the channel state information (CSI) acquisition scheme by considering the parametric sparsity and channel model in [27]. In [28], the authors studied Bayesian framework and provided some useful results and algorithms. In [29], ultra-wideband channel estimation is investigated by making use of Bayesian estimation theory. The authors also analyzed the performance and the application situations of this scheme.  
Although there are some works about the application of compressed sensing in underwater sensor networks [30; 31; 32; 33; 34], few studies focused on the effect of the sensor node selection scheme. For underwater sensor networks, the energy is strictly limited because the underwater sensor node can not be charged again. It is significant to consider the sustainability of the network when the sink node determines the selection set of sensor nodes. In addition, to obtain more accurate reconstruction results, the performance of reconstruction is worthy of studying. Motivated by the analysis above, we aim at providing a novel sensor node selection scheme for improving the reconstruction performance and the network lifetime. By making full use of the advantage of Bayesian theory, the mean square error (MSE) of estimation can be utilized to optimize the sensor node selection scheme.