In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.