Learning‐based design of random measurement matrix for compressed sensing with inter‐column correlation using copula function

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.