For non-ideal image construction performance of a block circulant matrix in remote sensing compressive imaging, this paper introduces the particle swarm optimization intelligent algorithm into optimizing the block circulant matrix, meanwhile maintaining the matrix structure. Firstly, the Welch bound of a correlation coefficient is taken as a threshold value to restrain the off-diagonal entries of the Gram matrix and to build a target matrix. Then, the objective function is established by making the Gram matrix approach the target matrix, and the optimized variable is replaced as the free entries to compose the block circulant matrix. To improve the optimized efficiency, the weight adaptive update is used to improve the partical search capacity. A construction comparison experiment is carried out, the results show that the correlation properties of the block circulant matrix with the sparse transform matrix has been reduced while maintaining the matrix structure, and the coefficients for maximum correlation, average correction and threshold average correction have been reduced by 0.027 3, 0.017 5 and 0.004 6, respectively. These results show the image construction performance is improved by optimized block circulant matrix.