Hybrid Reversible Data Hiding in Encrypted Satellite Images Using Fluctuation Modification Extraction and Reed-Solomon Code Embedding

In conventional hybrid reversible data hiding in encrypted images (RDHEI), the error-free extracted-bit rate condition in recovered images cannot be fully achieved (reversible) as the block size decreases because of the fluctuation function used, which cannot reduce the bit error, as indicated by the high extracted-bit error rate (EER) and low peak signal-to-noise ratio (PSNR). Therefore, this work proposes improving the accuracy of hybrid RDHEI performance for remote sensing satellite images by modifying the fluctuation function in the data extraction process with and without the Reed-Solomon (RS) codes in the data embedding process. The proposed fluctuation function takes the absolute difference in the actual value of two adjacent pixels in horizontal and vertical pixels. The modified fluctuation function algorithm in the extraction process both with and without RS codes in the embedding data process is derived, and performance results are obtained through simulations of SPOT-6, SPOT-7, and Pleiades-1A satellite images. The simulation results show that the proposed hybrid RDHEI algorithm with modification of the fluctuation function without an RS encoder can achieve error-free extracted-bit and maximum PSNR (infinity) values at a block size of
$18 \times 18$
for SPOT-6 and SPOT-7 test images, as well as a block size of
$20\times 20$
for the Pleiades-1A test image. It is proven that the proposed hybrid RDHEI succeeds in reducing the minimum block size from reference systems. In addition, it can also be seen that the proposed hybrid RDHEI with modification of the fluctuation function and RS coding in data embedding can reduce the minimum block size to achieve error-free extracted bits to
$9 \times 9$
for SPOT-6 and SPOT-7 test images and
$10\times 10$
for the Pleiades-1A test image.