Robust digital watermarking in the ridgelet domain

In this letter, we propose a multiplicative watermarking method operating in the ridgelet domain. We employ the directional sensitivity and the anisotropy of the ridgelet transform (RT) in order to obtain a sparse image representation, where the most significant coefficients represent the most energetic direction of an image with straight edges. Therefore, given a natural image, the associated edge image is obtained by means of a filter bank designed using the circular harmonic functions, then the edge image is partitioned into small blocks in order to deal with straight edges. Finally, the RT is performed for each block, the most relevant coefficients are selected, and eventually the watermark is embedded. Robustness and transparency are proven by experimental results.