A Novel Watermarking Method using Hadamard Matrix Quantization

Abstract

One of the most used watermarking algorithms is Singular Value Decomposition (SVD), which has a balanced level of imperceptibility and robustness. However, SVD uses a singular matrix for embedding and two orthogonal matrices for reconstruction, which is inefficient. In this paper, a Hadamard matrix is used to get a singular matrix for the reconstruction process. Moreover, SVD works with a floating-point value, which takes long processing time, while the Hadamard matrix works with an integer range, which is more efficient. Visual measurement showed that SVD and the new method had average NC values of 0.8321 and 0.8293, whereas the average SSIM values resulted in the same value (0.9925). In terms of processing time, the proposed method ran faster than SVD with an embedding and extraction time of 0.6308 and 0.2163 seconds against 0.8419 and 0.2935 seconds. The proposed method successfully reduced the running time while maintaining imperceptibility and robustness.

Fragile watermarking for image authentication using dyadic walsh ordering

“…The next step is to carry out an irregular attack on all these images and then an authentication process is carried out to find the modified region. The entire test is also measured by time parameters to compare the SVD [23], Hadamard [32], and the proposed method.…”

“…This research proposes improvements from the SVD block-based method proposed by Kang et. al [23] by developing the Walsh block from the Hadamard matrix in [32] to replace the U, S, V matrices, and block scrambling as shown in Fig. 3.…”

“…Therefore, this paper uses dyadic ordering which has binary changes of 1 bit in the successive rows. In addition, this rearrangement is also used to scramble the row sequence of the Hadamard [32] block so that the process of inserting bits can be carried out without a scrambling algorithm such as Arnold Transform [23]. The rows in Hadamard matrix in (2) are reordered to produce a Walsh matrix with a size of four 𝑊𝑊 4 which have successive rows of 0, 1, 3, and 2 sign changes as shown in (3):…”

“…Where 𝑆𝑆𝑆𝑆𝑆𝑆(𝐵𝐵) is an 𝑆𝑆𝑆𝑆𝑆𝑆 function that generates a singular matrix 𝑆𝑆 and two orthogonal matrices 𝑈𝑈 and V from the image block 𝐵𝐵. The value of the approach used can preserve the value of the bits embedded in an image because the image is not very sensitive to small changes in pixel values [32].…”

Fast image watermarking based on signum of cosine matrix

“…Whereas, the current need is a model with fast computational time, good robustness, and imperceptibility [20]- [22]. Combining several algorithms is not the best solution in optimizing imperceptibility, robustness, or processing time [23].…”