According the problem raised in compressive sensing theory that the classical measurement matrices (random Gaussian, random Bernoulli, etc.) does not achieve the optimal performance, the singular value decomposition is introduced in this paper, thus a novel method is proposed for the measurement matrix optimization based on singular value decomposition, to optimize the general linear measurement model in compressive sensing, i.e. measurement matrix and corresponded measurement vector, and then the original signal sparse signal is reconstructed by the optimized linear measurement model. Numerical results for the classical random Gaussian measurement matrix and random Bernoulli measurement matrix demonstrate that our proposed method can significantly increase the reconstruction probability of successful recovery and are more robust to Gaussian noise. Our proposed method is applicable to the general linear measurement system, which can successfully achieve the separation of the measurement matrix and the reconstruction matrix, and make the reconstruction matrix close to the most excellent configuration without the any model change at the front end of the measurement system.
