Reversible Watermarking in Medical Images Using Sub-Sample and Multiple Histogram Modification

Introduction

Reversible watermarking in digital image has been widely used in digital image copy right protection in recent years. Because of the reversibility of these algorithms that the cover image could be restored to the original state after the extraction of the watermark, reversible watermarking has been deeply studied in recent years. Existing reversible watermarking methods are mainly based on lossless compression(Maxwell, Handel et al. 1998, Shih and Wu 2005, Kountchev, Todorov et al. 2006), difference expansion (DE) (Tian 2003, Alattar 2004, Chang and Lu 2006, Lee, Wu et al. 2008, Lin, Tiegang et al. 2012), histogram shifting (HS)/histogram modification(HM) (Ni, Shi et al. 2006, Li, Zhang et al. 2015), prediction-error expansion (PEE) (Thodi and Rodríguez 2007, Fallahpour 2008, Chen, Chen et al. 2009, Tai, Yeh et al. 2009, Tsai, Hu et al. 2009, Luo, Chen et al. 2010, Chen, Sun et al. 2013).

The lossless compression based schemes first compressed the cover image using lossless compressing scheme. Then 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 cover image was reverse to the original state by decompressing the compressed image using the lossless compression algorithm.

Lossless compression based schemes are easily to achieve. However, the performance of these schemes highly effected by the performance of the lossless compression algorithm. The drawback of lossless compression based scheme are robustness and perceptional quality. This kind of scheme usually vulnerable against tampering attack. Moreover, since the cover image had been compressed, the visual quality of the stego-image is significantly deduced. This drawback made the lossless compression based scheme not suitable for the usage of reversible 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: