This paper presents an efficient reconstruction method in block compressed imaging (BCI) for natural images. To avoid the high complexity and give a time-efficient approach, block-based separable two-dimension (2D) linear reconstruction method is proposed. The techniques of adaptive sampling (AS) and separable reconstruction are combined to yield a competitive solution for BCI. The AS is utilized by employing more measurements in the texture redundant blocks. The separable 2D reconstruction uses linear approach based on minimum mean square error (MMSE) to reduce the decoder complexity. Experiment results demonstrate that the proposed scheme can efficiently reduce the reconstruction complexity and give a competitive image quality compared to non-linear approaches.