The stability of sparse reconstruction algorithms in compressed sensing can be raised by reducing the mutual coherence value of the equivalent dictionary， i.e.， the product of the measurement matrix and the sparsifying dictionary. While， the existing optimal design methods do not consider how to improve the efficiency of signal reconstruction when reducing the mutual coherence value. To overcome the problem， a constrained smooth optimization problem about measurement matrix is proposed， in which the first constraint requires the mutual coherence value of the equivalent dictionary to be as small as possible， and the second one uses the L₁ norm to facilitate the sparsity of the measurement matrix. Then， a convergent alternating projection algorithm is used to solve it. The simulation results on natural images show that compared with the equivalent dictionaries obtained by several existing optimal design methods， the proposed method greatly raises the sparsity of measurement matrix and improves the signal recovery accuracy.