Lossless cross-recovery of images with Reed-Solomon erasure codes
摘要
This paper proposes a lossless cross-recovery method for a group of digital images using Reed-Solomon (RS) erasure codes. For a given group of images, each image is first compressed using the JPEG XL compression standard to generate its corresponding recovery data. The recovery data of each image is then encoded using RS erasure codes to generate multiple shares based on a recovery threshold. The generated shares of each image are cross-distributed such that each image collects one share from each of the other images to form its shadow. The resulting shadows are then embedded in their corresponding original images to create stego-images. To ensure integrity, an authentication code is generated and embedded in each stego-image to produce the final watermarked images. If the number of reliable watermarked images meets or exceeds the recovery threshold, the damaged or lost watermarked images can be recovered from these reliable images. Moreover, with lossless JPEG XL compression and a suitable recovery threshold, the original images can be recovered without any loss. Experimental results on the Break Our Steganographic System Base (BOSSBase) and Uncompressed Color Image Database (UCID) datasets demonstrate that the proposed method achieves lossless cross-recovery while maintaining fault tolerance determined by the recovery threshold. Compared with existing threshold-sharing-based schemes, which only achieve lossy cross-recovery, the proposed method supports significantly larger image groups and avoids the storage overhead required by the previously reported multi-image recovery scheme.