Reversible Watermarking in Medical Image Using RDWT and Sub-Sample

Introduction

Digital watermark has been widely used in the copyright protection of digital image. In medical area, reversible watermarking scheme is more preferred than irreversible scheme because of the highly demand on the perceptional quality of the image. Based on the algorithm used to achieve reversible embedding, the reversible watermarking scheme could be categorized into three types: lossless compression based schemes, difference expansion (DE) based schemes and histogram shifting / histogram modifying (HS/HM) based schemes.

The lossless compression based schemes first compressed the cover image using lossless compressing scheme(Kountchev, Todorov, Kountcheva, & Milanova, 2006; Maxwell, Handel, & Bradley, 1998; Shih & Wu, 2005). After the compression the size of the cover image has been reduced, the watermark could be embedded into the image by exploit the space generated by the compression. During the extraction process, the watermark was extract from the image, then the compressed image was decompressed using the lossless compression algorithm.

Lossless compression based schemes are easily to achieve. The performance of these schemes is highly depends on the performance of the lossless compression algorithm. The draw back of lossless compression based scheme are robustness and perceptional quality. Because the compressed cover image is vulnerable to the tamper of the stego-image, this kind of scheme usually is not robust against tampering attack. Moreover, since the cover image had been compressed, the visual quality of the stego-image is significantly deduced, which made lossless compression based schemes not suitable for used in medical image watermarking.

Difference expansion based scheme was first proposed by Tian(Tian, 2003) .The main idea of Tian’s scheme is as follows: For an 8-bit grayscale image, a pixel pair (x, y) is used to embed a secret bit S,.In the embedding phase, the difference value h and the integer average value l are defined as:

The inverse transform is

Next, the new difference is obtained as follows:

Finally, the stego-pixel pair is obtained by the following transform:

In order to prevent underflow and overflow, the absolute of new difference after a secret bit S has been embedded must satisfy the following condition:

DE based scheme was initially proposed and used in spatial domain embedding. Since it is easy to achieve, lots of researches had been done and several improvements have been made based on Tian's scheme. For example, Alattar et al. introduced DE scheme into quad of pixels(Alattar, 2004). By expanding pairs to quads, Alattar's scheme improved the embedding capacity from 0.5 bpp to 0.75 bpp at best case. Other researches using the same method including Lee's(Lee, Wu, Tsai, & Chu, 2008) and Chang's (Chang & Lu, 2006) scheme. These schemes tried to expand pairs of pixels to quads or even more pixels. These improved schemes could generate more differences than original DE scheme, which means higher embedding capacity.