Fragile watermarking using Karhunen–Loève transform: the KLT-F approach

The paper presents a fragile watermarking technique that may be used to discover image manipulations at block level. The proposed algorithm, based on the Karhunen–Loève linear transform (KLT), modifies some of the KLT coefficients obtained from a secret base (defined by a secret key image) so that they contain a binary pseudo-random message. A genetic algorithm is used to compensate for rounding errors introduced by inverse transforming in the integer pixel domain. An extensive experimentation has been performed to test the effectiveness of the method and to show the sensitivity of the algorithm to single pixel modifications (also as a function of the number of modified coefficients). A comparison with other fragile watermarking methods is reported. It should be noted that the proposed approach results in both a high PSNR (more than 53 dB on average) and a high subjective quality. The system may be tested online by submitting images to be watermarked and subsequently verifying the presence of modifications in a previously marked image.