To enhance the tampering localizability of image authentication, a new fragile watermarking scheme, which exploits the perturbation in reverse processing, is proposed. In verifying data integrity, the new method performs the reverse processing of watermark embedding. Typically, it de-filters the distributed version or equivalently solves an embedding equation. If any tampering happened, the output of the method perturbs because the manipulated data, which can be regarded as the observing error, is drastically enlarged by such processing. The perturbed values indicate the degree of tampering, and their positions directly draw the shapes of the manipulated areas. Compared with the mostly used block-based methods, the new method localizes the tampering almost pixel-wise instead of block-wise. It also supports the popular adaptive embeddin, which does not evenly embed the watermark.