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Existed inherent sparsity of natural images in some domains helps to reconstruct the signal with a lower number of measurements. To benefit from the sparsity, one should solve the reweighted $\ell_{1}$-norm minimization algorithms. Although, the existed reweighted $\ell_{1}$-norm minimization approaches work well for k-sparse signals, but, the performance of these methods for compressible signals are not competitive with unweighted one.

Recently, multidimensional signal reconstruction using a low number of measurements is of great interest. Therefore, an effective sampling scheme which should acquire the most information of signal using a low number of measurements is required. In this paper, we study a novel cube-based method for sampling and reconstruction of multidimensional signals. First, inspired by the block-based compressive sensing (BCS), we divide a group of pictures (GoP) in a video sequence into cubes. By this way, we can easily store the measurement matrix and also easily can generate the sparsifying basis.

This paper considers the channel state information (CSI) acquisition and exploitation problem in cloud radio access networks (Cloud-RAN). A novel CSI acquisition method, called compressive CSI acquisition, is adopted to effectively reduce the CSI signaling overhead by obtaining instantaneous coefficients of only a subset of all the channel links.To deal with the uncertainty in available CSI, we propose a stochastic power control (SPC) framework, which is a highly intractable joint chance constrained program (JCCP).