基于NSCT与约束NMF的抗干扰图像融合水印算法

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本文探讨了一种基于Non-Subsampled Contourlet Transform (NSCT) 和约束非负矩阵分解（Constrained Non-negative Matrix Factorization, CNMF）的图像融合水印算法。发表在《信号处理、图像处理与模式识别》(International Journal of Signal Processing, Image Processing and Pattern Recognition) 的2015年第8卷第1期，页码69-78，DOI为10.14257/ijsip.2015.8.1.07，ISSN为2005-4254。该研究由西安医学院计算机工程学院的谢敏(Xianmin Wei)和彭章(Peng Zhang)共同完成，通讯地址位于中国潍坊东风东路5147号。研究背景是为了解决Contourlet变换中的混叠（aliasing）问题，作者提出了一种新的方法。该算法分为三个主要步骤： 1. 图像分解：首先，对原始图像进行NSCT分解，将图像分割成多个子带或层次，每个子带对应不同的频率成分，有助于提取关键信息并减少低频区域的干扰。 2. 构建低频矩阵：接着，利用低频系数（通常包含更多的图像结构信息）和嵌入的水印信号构建一个二维矩阵。低频系数的选择有助于增强水印的嵌入效果，而水印信号则被巧妙地融入其中。 3. 水印嵌入：通过CNMF进行嵌入操作。CNMF是一种非负矩阵分解技术，它在保持数据非负性的同时进行特征学习，这使得嵌入的水印能够在不影响图像视觉质量的同时保持良好的不可见性。 4. 盲检测与鲁棒性：算法采用盲检测方法来验证嵌入的水印，即使在经过常见的图像处理攻击（如缩放、旋转、裁剪等）后，仍能有效地检测出水印的存在，体现出很高的鲁棒性。 5. 实验结果与评价：实验结果显示，该算法在保证图像融合质量和水印不可见性的前提下，具有良好的抗攻击性能，适合于数字版权保护和信息安全领域应用。关键词包括：数字水印、非抽样轮廓线变换（Non-Subsampled Contourlet Transform）、非负矩阵分解（Non-negative Matrix Factorization）、图像融合、盲检测以及鲁棒性。这篇研究提供了一个创新的解决方案，提高了图像水印技术的实用性和安全性。

International Journal of Signal Processing, Image Processing and Pattern Recognition

Vol. 8, No. 1 (2015), pp. 69-78

http://dx.doi.org/10.14257/ijsip.2015.8.1.07

ISSN: 2005-4254 IJSIP

Image Fusion Watermarking Algorithm based on NSCT and

Constrained NMF

Xianmin Wei

and Peng Zhang

1.2

School of Computer Engineering, Weifang University

5147 Eastern Dongfeng Street, Weifang 261061, China

wfxyweixm@126.com

Abstract

In order to solve the problem aliasing of Contourlet transform, an Image Fusion

Watermarking Algorithm based on NSCT and constrained NMF is proposed in this paper.

Firstly, the image is decomposed into several layers. Secondly, the Two-dimension matrix

is obtained by low frequency coefficients and watermarking signal. Finally, the

watermarking is embedding by constrained NMF. The blind detection is used, and the

algorithm can achieve a good imperceptibility. Experimental results show that the

algorithm has good robustness against attacks of common image processing.

Keywords: Digital watermarking, Non-subsampled Contourlet Transform (NSCT),

Non-negative Matrix Factorization (NMF), Image fusion

1. Introduction

Features of digital images easily spread and replicated have made worse image content

infringing, tampering, forgery and other growing problem, the image content information

security has become a problem to be solved lately. Digital watermarking is a technology

embedded in the multimedia data having imperceptible, robust, resisting detectability and

which contains digital coding technology of sensitive information authentication, mainly

used for addressing the identification mark provided in digital media copyright protection

problem [1]. As an emerging discipline, the digital watermarking in the communications,

computer, cryptography has achieved a wide range of applications, which is an effective

way to solve the above problems.

In 2002, M.N.Do and M. Vetteri [2, 3], who proposed the outline wave-Contourlet

transform, Contourlet transform is a real image two-dimensional representation, which

provides a flexible multi-scale, local, directional the analytical method, and which can

more fully demonstrate the geometric characteristics of the image itself. Contourlet

transform will be applied once appeared in the field of digital watermarking, and made a

series of studies [4, 5]. But smoothness of Contourlet transform basis functions is not

ideal; spectrum aliasing exists in low-frequency sub-band, high-frequency sub-band and

each directional sub band. In 2006, for some limitations A.L.Cunha improved Contourlet

transform, and proposed a non-sampling Contourlet Transform (Non-subsampled

Contourlet Transform, NSCT) [6] method, NSCT is a shift-invariant, multi-scale, multi-

direction super complete transformation [7], compared with Contourlet transform, smooth

and high NSCT basis functions has no spectral aliasing, and it has stronger direction

selectivity.

For presence of confusion problem in Contourlet transform spectrum, this paper

designed a fusion of non-sampling Contourlet transform watermark and constraints NMF

algorithm based on a combination of image. Watermark information by NMF embedded

into the image fusion among NSCT decomposition coefficients. Compared with the

traditional NMF, constrained NMF has low computational complexity, good separation

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