Abstract: Because of existing Compressed-Sensing (CS) reconstruction algorithms have high computing complexity, a fast algorithm based on best linear estimate is proposed. It adaptively measures image data with a block-by-block manner at encoder, and reconstructs each block at decoder using the best linear operator which is constituted by statistical autocorrelation function matrix estimated according to various statistical property of image block. This algorithm replaces lots of nonlinear iterations in traditional CS reconstruction algorithm with linear projection, therefore it shorten the time of recovering image. Simulation experimental results indicate that the proposed algorithm not only reduces the time of rebuilding image, but also is better than the current popular CS reconstruction algorithm for images containing uncomplicated textures on the reconstructed image quality.