In this work, we firstly investigate directional lifting wavelet transform (DLWT) as a sparse representation of images. Then a block compressive sensing (BCS) measurement matrix is designed by using the generalized Gaussian distribution (GGD) model. The measurement matrix can be used to sense the DLWT coefficients of images, which reflects the feature residual introduced by steganography. Finally, a reconstruction approach of hidden signal is achieved efficiently by the extracted residual. With the residual message, the scheme has a flexible self-recovery quality. Experimental results show that our proposed method is not only universal for detecting spatial domain steganography, but also capable of recovering the secret signal from the stego images.