Watermarking Scheme With Bounded-Exhaustive Self-Recovery Approach

This paper revisits a fragile watermarking scheme with exact self-recovery capabilities and proposes a novel restoration process. The restoration mechanism is aimed at solving Systems of Binary Linear Equations (SBLE) associated with altered subsets of bits, using arithmetic module-2. The chances that those SBLE will be linearly dependent increase for more significant tampering rates. While such subsets are deemed to be unrecoverable by schemes in the current watermarking literature, the proposed restoration process calculates the Hermite standard form of the matrix representation of the SBLE to find both the pivot and the free variables. Since the number of solutions is finite when using arithmetic module-2, all the answers are calculated by exhaustively replacing the free variables with all the possible combinations of bits. Finally, the solutions are analyzed to possibly restore some tampered bits to enhance the recovery performance in every iteration. Experimental results demonstrate that the proposed scheme outperforms the best methods with exact self-recovery capabilities in the state-of-the-art in terms of embedding time, restoration time, and restoration performance.