In this paper, we consider the problem of sparse signal recovery using a learned dictionary in multiple measurement vectors (MMVs) case. Employing deep neural networks, we provide two new greedy algorithms to solve sparse MMV problems. In the first algorithm, we create a stacked vector of measurement matrix columns and a new measurement matrix, which can be assumed as the Kronecker product of the primary compressive sampling matrix and a unitary matrix. In order to reconstruct sparse vector corresponding to this new set of equations, a four-layer feed-forward neural network is applied. In the second algorithm, joint sparse structure of the sparse vectors is considered. Recurrent neural networks are employed to extract the joint sparsity structure. In addition, we utilize an over-complete dictionary obtained from an unsupervised learning procedure. Simulation results illustrate the benefit of using the proposed methods. Finally, the proposed algorithms are applied for pilot-based channel estimation in massive multiple-input multiple-output systems to improve the channel state information recovery performance.

在本文中，我们考虑了在多个测量向量（MMV）情况下使用学习词典进行稀疏信号恢复的问题。利用深度神经网络，我们提供了两种新的贪婪算法来解决稀疏MMV问题。在第一种算法中，我们创建了一个测量矩阵列的堆叠矢量和一个新的测量矩阵，可以将它们假定为主压缩采样矩阵和and矩阵的Kronecker乘积。为了重建对应于这组新方程组的稀疏矢量，应用了四层前馈神经网络。在第二种算法中，考虑了稀疏矢量的联合稀疏结构。采用递归神经网络提取联合稀疏结构。另外，我们利用从无监督学习过程中获得的过度完整的字典。仿真结果说明了使用所提出方法的好处。最后，将所提出的算法应用于大规模多输入多输出系统中基于导频的信道估计，以提高信道状态信息的恢复性能。