Image steganography plays a vital role in securing secret data by embedding it in the cover images. Usually, these images are communicated in a compressed format. Existing techniques achieve this but have low embedding capacity. Hence, the goal here is to enhance the embedding capacity while preserving the visual quality of the stego-image. It is also intended to ensure that the scheme is resistant to steganalysis attacks. This paper proposes a compressed sensing image steganography (CSIS) scheme to achieve these goals. In CSIS, the cover image is sparsified block-wise, linear measurements are obtained, and then permissible measurements are selected. Next, the secret data is encrypted, and 2 bits of this encrypted data are embedded into each permissible measurement. For the reconstruction of the stego-image, ADMM and LASSO are used for the resultant optimization problem. Experiments are performed on several standard greyscale images and a colour image. Higher embedding capacity, 1.53 times more compared to the most recent scheme, is achieved. An average of 37.92 dB PSNR value, and average values close to 1 for both the mean SSIM index and the NCC coefficients are obtained, which is considered good. These metrics show that CSIS substantially outperforms existing similar steganography schemes. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.