Compressive sensing (CS) is a new efficient framework for sparse signal acquisition, which has been widely used in many application fields, such as multimedia coding and processing, etc. In this paper, a novel block-based compressive sensing scheme for robust image compression applications is proposed, where the relative sparsity of image chunks are exploited to effectively allocate sensing resources to different image blocks. The image is split into non-overlapping blocks of fixed size, which are independently represented by compressive sensing in the discrete cosine transform (DCT) domain. The key idea is to assign more sensing resources to the image blocks with rich edge and texture features but less to the image blocks located at smooth regions. Simulation results for standard compression test images demonstrate that the proposed scheme can get significant performance gain in reducing measurement rate and/or enhancing reconstructed image quality.