The existing image compression methods (e.g., JPEG2000, etc.) are vulnerable to bit-loss, and this is usually tackled by channel coding that follows. However, source coding and channel coding have conflicting requirement. In this paper, we address the problem with an alternative paradigm, and a novel compressive sensing (CS) based compression scheme is therefore proposed. Discrete wavelet transform (DWT) is applied for sparse representation, and based on the property of 2-D DWT, a fast CS measurements taking method is presented. Unlike the unequally important discrete wavelet coefficients, the resultant CS measurements carry nearly the same amount of information and have minimal effects for bit-loss. At the decoder side, one can simply reconstruct the image via l1 minimization. Experimental results show that the proposed CS-based image codec without resorting to error protection is more robust compared with existing CS technique and relevant joint source channel coding (JSCC) schemes.