Two properties of SVD and its application in data hiding

Abstract

In this paper, two new properties of singular value decomposition (SVD) on images are proved. The first property demonstrates the quantitative relationship between singular values and power spectrum. The second one proves that under the condition of losing equal power spectrum, the squareerror of the reconstructed image is much smaller when we reduce all singular values proportionally instead of neglect the smaller ones. Based on the two properties, a new data-hiding scheme is proposed. It performs well as for robustness, for it satisfies power-spectrum condition (PSC), and PSC-compliant watermarks are proven to be most robust. Besides, the proposed scheme has a good performance as for capacity and adaptability. © Springer-Verlag Berlin Heidelberg 2007.