In this work, a novel learning-based approach for the design of a compressed sensing measurement matrix is proposed. In contrast with the state-of-the-art methods, the suggested approach takes into account the correlation within entries of each column of the measurement matrix, namely, the inter-column correlation (ICC). The new method makes use of a rather small number of training sparse signal vectors in a recursive scheme to obtain their corresponding measurement vectors. The latter is exploited to estimate the copula function of measurements which, in turn, is used to generate an arbitrary number of measurement vector ensembles. By using the latter, the autocorrelation of the measurement vectors is estimated precisely and then, the ICC of measurement matrix under design is obtained from the autocorrelation. Given the resulting ICC, the measurement matrix columns are to be generated independently, e.g. by employing a proper random Gaussian vector generator. Performance evaluations using both synthetic and real-world data confirm the superiority of the proposed approach to the less recent methods.

中文翻译：

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基于学习的基于copula函数的列间相关压缩感知随机测量矩阵设计

在这项工作中，提出了一种新颖的基于学习的压缩感知测量矩阵设计方法。与最新方法相反，建议的方法考虑到了测量矩阵每一列条目内的相关性，即列间相关性（ICC）。新方法在递归方案中使用了相当少的训练稀疏信号向量，以获得它们相应的测量向量。后者被用来估计测量的copula函数，然后又用于生成任意数量的测量矢量集合。通过使用后者，可以精确估计测量向量的自相关，然后从自相关中获得设计中的测量矩阵的ICC。根据产生的ICC，测量矩阵列将独立生成，例如通过使用适当的随机高斯矢量生成器。使用综合数据和实际数据进行的性能评估证实了所提出方法相对于较新方法的优越性。