Robust Secret Image Sharing Resistant to Noise in Shares

A secret image is split into shares in the generation phase of secret image sharing (SIS) for a threshold. In the recovery phase, the secret image is recovered when any or more shares are collected, and each collected share is generally assumed to be lossless in conventional SIS during storage and transmission. However, noise will arise during real-world storage and transmission; thus, shares will experience data loss, which will also lead to data loss in the secret image being recovered. Secret image recovery in the case of lossy shares is an important issue that must be addressed in practice, which is the overall subject of this article. An SIS scheme that can recover the secret image from lossy shares is proposed in this article. First, robust SIS and its definition are introduced. Next, a robust SIS scheme for a threshold without pixel expansion is proposed based on the Chinese remainder theorem (CRT) and error-correcting codes (ECC). By screening the random numbers, the share generation phase of the proposed robust SIS is designed to implement the error correction capability without increasing the share size. Particularly in the case of collecting noisy shares, our recovery method is to some degree robust to some noise types, such as least significant bit (LSB) noise, JPEG compression, and salt-and-pepper noise. A theoretical proof is presented, and experimental results are examined to evaluate the effectiveness of our proposed method.