  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.
Enhancing this capacity causes a deterioration in the visual quality of the
stego-image. Hence, our goal here is to enhance the embedding capacity while
preserving the visual quality of the stego-image. We also intend to ensure that
our scheme is resistant to steganalysis attacks.
  This paper proposes a Compressed Sensing Image Steganography (CSIS) scheme to
achieve our goal while embedding binary data in images. The novelty of our
scheme is the combination of three components in attaining the above-listed
goals. First, we use compressed sensing to sparsify cover image block-wise,
obtain its linear measurements, and then uniquely select permissible
measurements. Further, before embedding the secret data, we encrypt it using
the Data Encryption Standard (DES) algorithm, and finally, we embed two bits of
encrypted data into each permissible measurement. Second, we propose a novel
data extraction technique, which is lossless and completely recovers our secret
data. Third, for the reconstruction of the stego-image, we use the least
absolute shrinkage and selection operator (LASSO) for the resultant
optimization problem.
  We perform experiments on several standard grayscale images and a color
image, and evaluate embedding capacity, PSNR value, mean SSIM index, NCC
coefficients, and entropy. We achieve 1.53 times more embedding capacity as
compared to the most recent scheme. We obtain an average of 37.92 dB PSNR
value, and average values close to 1 for both the mean SSIM index and the NCC
coefficients, which are considered good. Moreover, the entropy of cover images
and their corresponding stego-images are nearly the same.
