Optimization of Robust Measurement Matrix Based on Improved Target Gram Matrix
The optimization of the measurement matrix is an important part of compressed sensing.The design of the target Gram matrix and the update of the measurement matrix are two important steps in the optimization of the measurement matrix.However,in the current optimization models,the effects of the two steps cannot be optimal at the same time,and how to optimize the effects of the two important steps at the same time has become an urgent problem to be solved.Aiming at this problem,a robust measurement matrix optimization method based on improved target Gram matrix is proposed.Firstly,the superiority of the adopted target Gram matrix is proved,that is,overall reduction of three mutual coherences between measurement matrix and sparse basis;Secondly,the superiority of the adopted measurement matrix update method is proved,that is,reduction of the sparse error and improvement of robustness of the measurement matrix;Finally,the optimal target Gram matrix is applied to the optimal measurement matrix update method,which improves the signal reconstruction accuracy.The experimental results show that,the measurement matrix optimization method proposed in this paper effectively improves the reconstruction quality of two-dimensional signals.
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