A Novel Digital Watermarking Based on General Non-Negative Matrix Factorization

In this paper, we propose a novel general non-negative matrix factorization (general-NMF)-based digital watermarking scheme for copyright protection and integrity authentication of the image content. Specifically, the proposed general-NMF algorithm is able to factorize a matrix <inline-formula><tex-math notation="LaTeX">$C\in R_+^{s\times t}$ </tex-math></inline-formula> into a basis matrix <inline-formula><tex-math notation="LaTeX">$A\in R_+^{m\times n}$ </tex-math></inline-formula> and a coefficient matrix <inline-formula><tex-math notation="LaTeX">$B\in R_+^{p\times q}$ </tex-math></inline-formula> by removing the dimension-matching constraints required by the conventional NMF, where <inline-formula><tex-math notation="LaTeX">$s=m$</tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$n = p$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">$t= q$ </tex-math></inline-formula>. In particular, <inline-formula><tex-math notation="LaTeX">$s= m\cdot l/n$</tex-math> </inline-formula>, <inline-formula><tex-math notation="LaTeX">$t=l/p\cdot q$</tex-math></inline-formula>, and the variable <inline-formula><tex-math notation="LaTeX">$l$</tex-math></inline-formula> is the least common multiple of <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$p$</tex-math></inline-formula>. Furthermore, the generator factor of the random matrix and <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> are used as the keys of the proposed digital watermarking scheme. Experimental results show that the proposed digital watermarking scheme can effectively resist various attacks and tampering.

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