## 2 Energy Conservation Schemes in WSN  
Several energy conservation/saving schemes have been proposed for WSNs. WSN-based signal acquisition using CS is discussed in [6]. The correlations among signals detected by different sensors are explored to further reduce the amount of samples required for reconstruction. Environmental data gathered by a WSN located in the Intel Berkeley Research Lab [7] are considered in [6]. Spatial correlation of the sensed signal is explored in [8] in order to propose a compressive-based sleeping WSN, in which a TDMA scheme is employed imposing only a fraction of the sensor nodes to be active in each time slot. Data gathered by the active nodes are transmitted to a base station and data corresponding to the sleeping nodes are estimated from others. A cluster-based energy-efficient data collection by using the CS framework is proposed in [9]. The WSN is divided in clusters using two distinct communication models: In the first one, sensor nodes send their measurements to the cluster head that forwards the CS measurements directly to a Base Station; the second method uses intermediate cluster heads to forward CS measurements to the base station. Authors calculate the power consumption for both methods. A belief propagation algorithm [10] is considered in [11] to reconstruct CS measurements sent by sensor nodes, and iterative message passing is used to find the solution. A star topology is considered, in which sensor nodes directly send their CS measurements to the sink. WSN employ digital communication, consequently coefficients derived from sensor measurements must be quantized before transmission. However, the analyses performed in [6; 8; 9; 11] disregard this aspect, assuming that coefficients are densely quantized. Some insight on the quantization of compressive sensed measurements is presented in [12; 13; 14]. In [12], the 1-bit Compressive Sensing framework is proposed, which preserves only the sign information of each random measurement and the signal is recovered within a scale factor. This 1-bit CS framework is applied to data gathering in WSNs in [15]. In [13], an empirical analysis of the rate-distortion performance of CS is presented, in the context of image compression. The average distortion introduced by quantization on CS measurements is studied in [14] by comparing two reconstruction algorithms, the Basis Pursuit [16] and the Subspace Pursuit [17] CS recovery schemes. In [18], a CS-based coding technique that considers a binned progressive quantization framework in order to overcome the poor performance of CS applied to image compression is presented. The decoder firstly generates an initial reconstructed image, then quantization refinement occurs in order to subsequently improve the reconstructed image. The finer the quantization of the coefficients, the more bits are required for their transmission. In the present work, the amount of energy spent for transmission is considered a critical issue since one desires to consume the less energy while guaranteeing the best representation of the monitored signal; and both aspects will depend upon the CS-coefficients quantization scheme. Authors in [19] address the dimensionality reduction problem, applied to hyperspectral images, by using manifold learning methods. They propose the UL-Isomap scheme, in order to solve the main problems of the LIsomap method [20]: The shortcoming of random landscape and the slow computation speed of LIsomap. A Vector Quantization is considered to improve the landmark selection, and the computational speed of LIsomap scheme is accelerated by using random projections, in order to reduce the bands of HSI data. In [21], authors consider the nonlinear dimensionality reduction problem, also applied to hyperspectral image classification, and propose an Enhanced-Local Tangent Space Alignment (ENH-LTSA) method. As the work in [19], this proposed scheme applies random projections to reduce the dimension of HSI data, improving the construction of the local tangent space.