Aiming at the heavy difficulty or high cost for the random orthogonal matrix which used in separable compressive sensing for high-dimensional signals sensing, such as large-scale image compressive reconstruction, deterministic measurement matrices was introduced, and a separable compressive sensing using deterministic matrices was proposed, matrix with deterministic structure, such as Toeplitz or Circulant matrix, could be used as a left/right separable matrix in separable compressed sensing. The proposed scheme can significantly reduce the number of independent elements, thus significantly reduce the difficulty and the cost of physical implementation. Numerical simulations evaluated comparisons of reconstruction performance of the proposed method with different downsampling rates and different image sizes. The results indicate that the proposed method can achieve similar reconstruction quality with far fewer independent elements as random orthogonal matrix′s, which demonstrates the feasibility of the proposed method.