A blind digital image watermarking method based on the dyadic wavelet packet transform and fast interval arithmetic techniques

We propose a new digital image watermarking method based on the dyadic wavelet packet transform (DYWPT) and fast interval arithmetic (IA) techniques. Because the DYWPT has a redundant representation, like the dyadic wavelet transform (DYWT), the amount of information that the watermark must contain is greater than in the case of methods based on ordinary discrete wavelet transforms (DWTs) and the discrete wavelet packet transform (DWPT). However, the order of the high frequency components is not necessarily the same as the order of their frequency domain. Therefore, in our approach, we rearrange the order of the high frequency components in descending order of frequency components and embed a watermark selectively into higher frequency components. Our watermark is a ternary-valued logo that is embedded into higher frequency components through use of the DYWPT and fast IA techniques. We describe our watermarking procedure in detail and present experimental results demonstrating that our method produces watermarked images that have better quality and are robust with respect to various types of attacks, including marking, clipping, median filtering, contrast tuning (histeq and imadjust commands in the MATLAB Image Processing Toolbox), addition of Gaussian white noise, addition of salt & pepper noise, JPEG and JPEG 2000 compressions, rotation, and resizing.