# A Robust Multi-Watermarking Algorithm for Medical Images Based on DTCWT-DCT and Henon Map
## 1 Introduction
[11], using Laplacian and a horizontal set segmented the medical images into ROI and RONI, whereby the watermark information was embedded into a RONI based on Contourlet transformation and singular value decomposition (SVD); [PERSON] et al. [12] proposed a blind hybrid watermark algorithm for MRI images, which used a histogram to divide the image into ROI and RONI, and embedded the watermark into the RONI's spatial and wavelet domains; [PERSON] et al. [13] looked for RONI using saliency to find the smallest overlap with the ROI. When embedding, discrete wavelet transform and discrete cosine transformation (DWT-DCT) is used with redundant watermarks. When extracting, a vote is used. (2) The second category is based on reversible watermarking. [PERSON] et al. [14] proposed a new technique named IRW-Med', using the concept of a compression function to reduce the embedding distortion, and the integer wavelet transform (IWT) as an embedded domain to realize the reversibility of the watermark; [PERSON] et al. [15] introduced two innovative reversible algorithms, which were both based on a histogram shift to improve the hidden capacity, and to divide the image into non-overlapping blocks to embed the watermark; [PERSON] et al. [16] proposed a reversible watermarking scheme using quantization functions embedded in multiple watermarks and a novel tracking key to restore original medical images; [PERSON] et al. [17] inserted data and signature information into the original medical image via a recursive modulation algorithm after wavelet transform and singular value decomposition. In this method, the watermark strength is controlled by differential evolution. (3) The final category is based on classical conventional digital watermarking. In the literature [18; 19; 20; 21; 22], an algorithm of multiple watermarks for medical images is implemented. [PERSON] [PERSON] et al. [18] used SVD, DCT, DWT respectively for different type of watermarks, and back propagation neural networks (BPNN) to eliminate the impact of noise when extracting watermarks; they also enhanced its security by using Arnold transform; [PERSON] et al. [19] used fast discrete curvelet transform (FDCuT) for medical images to obtain the different frequency coefficients of the curve decomposition, and adopted DCT for high frequency coefficients. Then, the watermark is modified according to the medium frequency coefficient of a white gaussian noise (WGN) sequence image. During extraction, the same sequence of correlation is used to achieve blind recovery; [PERSON] et al. [20] proposed a new kind of multi-watermark which is controlled by secret key. The proposed hybrid decoder is optimal and locally optimal. It follows multiple multiplication rules and is based on the minimum risk of bayes. Their DWT coefficients are modeled as generalized gaussian distributions; [PERSON] et al. [21] proposed a local multi-watermark algorithm, which used the the robust and adaptive feature detector based on daisy descriptor (RAF3D) design adaptive detector to embed multiple watermarks into the orthogonal space of a feature extraction region at the same time. When extracting, the image can be extracted independently; [PERSON] et al. [22] proposed a spread spectrum watermarking algorithm, which used a haar wavelet to perform the binary sub-band decomposition, and then embedded different forms of watermark information in the intermediate frequency and second order selected frequency bands of the first order DWT respectively, according to the different contexts in which it was used. The three categories are shown in Figure 1.  
For algorithms based on the first and third categories, the embedding of watermarks affects the images themselves, and these watermarking algorithms have poor anti-geometric attack capabilities; they cannot even resist the tiny geometric transformations [9; 10; 22; 23; 24].