A Robust Non-Blind Watermarking for Biomedical Images Based on Chaos

The advent of the Internet in these last years encouraged a considerable traf-fic of digital images. In the sanitary field, precisely in telemedicine branch, medical images play a very important role for therapeutic diagnoses. Thus, it is necessary to protect medical images data before transmission over the network to preserve their security and prevent unauthorized access. In this paper, a secure algorithm for biomedical images encryption scheme based on the combination of watermarking technique and chaotic function is proposed. In the proposed method, to achieve high security level performances, a non-blind hybrid watermarking technique with audio signal, Discrete Wavelet Transform is used; smoothness is also used as selected criteria; the iterations obtained by the chaotic sequences are essential and allow a good realization of the encryption process. One of the main advantages of chaos-based encryption schemes is the generation of a large number of key spaces to resist brute force attacks from the encryption algorithm. The experimental results presented in this paper attest to the invisibility and robustness of the proposed algorithm combining watermarking and chaos-based encryption.


Introduction
Numerous different approaches for watermarking methods and image encryption can be found in the scientific literature [7], use watermarking to provide confidentiality of some images. In the same way [8], proposed a technique of watermarking for authentication, the method use wavelet decomposition.
Many others researchers as Puech et al. [9], proposed a robust watermarking algorithm with a combination of AES encryption to promote the confidentiality and integrity of medicals images. Gokcen et al. [10], proposed a robust chaotic digital image Watermarking Scheme based on RDWT and SVD. [11] [12] [13] and [14], have make use of watermarking to insert the information of patient.
Some others researchers as [15] [16] [17] [18] have apply many transformations as wavelet, wavelet packet transform, discrete cosine transform, Zernike moments in their proposed watermarking scheme. [19] proposed security technique based on watermarking and encryption for digital imaging and communication in medicine, including partial encryption methods. [20] proposed algorithm for coding, to determine a set of selective blocks for steady embedding. [21] had proposed a scheme which incorporates the concept of modular arithmetic and chaos theory, for image encryption and decryption. [22] used DCT to propose a blind watermarking algorithm; the phase of extraction is focused to the statistical properties of embedded sequence. [23] proposed a watermarking algorithm, where watermark is embedded in the most significant frequency of DFT of the host image. [24] proposed a watermarking scheme based on Wavelet Discrete Transform (DWT) and Logistic map to generate a binary watermark. Their proposed algorithm is blind watermarking algorithm. [25] proposed an efficient and secure algorithm, by associating chaos encryption and compression, the encryption is proceeding by diffusion and confusion properties.
Of the above works, we note that watermarking can be used to provide authentication, it also helps of adding necessary and personals information confidentially. In medicine milieu the combination of watermarking and encryption is essential to attempt two important criteria of medicals images security which are authentification and confidentiality. Robustness against attacks, imperceptibility, high capacity watermark embedding, security, reversibility and rapidity are also other criteria that we try to satisfy during the transmission of biomedical images all over the network transmission channels. The proposed algorithm in this paper satisfies some of these criteria.

Wavelet Discrete Transform (DWT)
Wavelet transform 2D, all as the other transformed Fourier 2D, cosine 2D is Discrete wavelet transform is characterized at time by its limit temporal and frequential (compact support). The decomposition of a signal x(l) to place through filters and gets itself in a following manner h(l) and g(l) are respectively High and low filters The obtained coefficients are: The image which is a signal of two dimension, its application of 2D wavelet transform gives a dyadic decomposition of this one with the help of a couple of quadratic mirrors filters (QMF)a being a High pass filter (HS) and the other a low pass (L). The use of does one coins sampling by a factor 2, permitting to get four sub-bands, one under-strip low frequency (LL) and three under-strips high respective frequencies (LH, HL,HH),representing, orientations with very specific vertical, horizontal and diagonal Face [26].

Discrete Cosine Transform (DCT)
It permits to separate the low frequencies from the high frequencies. This decomposition is done by dividing in blocks of 8 × 8 pixels according to the following equation: The inverse transform is obtained as:

Relative Smoothness
Measurement of relative smoothness is one of selected applications; it is made by the following relation: where, σ is the standard deviation of the gray values. x represent sub block of the image; biggest is relative smoothness better is the smooth of chosen block. In this paper relative smoothness is use as selected criteria for the four sub-images of second level decomposition of host image by wavelet discrete transform [27].

Watermarking
The watermarking image consists of inserting in an indelible manner, information in a host image then to tempt to recover this information after transfer [28].
The diagrams of watermarking are varied according to their application domain.
The insertion of the signature will make itself either in the spatial domain either in the transform domain. In additive diagram, information to insert is added in a picture whereas in a substitutive diagram information to insert is substituted for features of the picture. In our work we use an additive diagram in frequential domain. Equation gives an example: With W K marked bock image, X K , original image block, α mark strength, X W,K watermarked image.

Vershult Model
The model of Vershult is a model of growth proposed by Pierre François Vershult [29]. This model uses the functions refine to explain the birth rate and the death rate of a population. Putting x as carves of the population; m(x) the death rate and n(x) the birth rate. The size of the population follows the differential equation: If m and n are affine functions respectively increasing and decreasing functions. If, on the other hand, for x tending towards 0 growths is positive, the equation becomes: with a and b two real positive. Then, by setting K = a/b, the Equation (12) becomes: The constant K affects solution of this Equation (13) It is shown that: • The constant function K is a solution of this equation • If x < K then the population grows • If x > K then the population decreases.
The discrete resolution of the transformed Equation (13) is: if we put Equation (16)

Proposed Model
The paragraph below, presents the watermarking scheme associating the logistic map. The block diagram is illustrated in Figure 1; in order to better understand

Embedding and Encryption Algorithm
Watermark embedding and encryption are described as follows: Input: Host_object, Watermark Output: Encrypted_Object Step 1: Read grey scale Host_object of size M × N.
Step 4: Calculate relative smoothness (R) of four LL2, HL2, LH2, and HH2, choose the sub-band that has the biggest value of smoothness, HH2.
Step 5: Read audio signal, converted in 2D, call watermark of size m × n.
Step 10: Generate chaotic sequence with following parameters: µ = 3.93695629844, and initial x 0 = 0.456 Step 11: Generate n-iterations with logistic map to get h(i) different orbit: Step 12: Associate the chaotic sequence with pixels of watermarked; Step 13: Make permutation in lines, by N-iterations; Step 14: Make permutation in columns by M-iterations and get encrypted image; Step 15: Display Encrypted_objet.

Decryption and Extraction Algorithm
Input: Encrypted Object, Host object, Output: Extracted Watermark; Step 1: Read Encrypted Object.

Results and Discussion
Various experiments are carried out to assess the performance of the proposed algorithm, in terms of robustness against attacks and imperceptibility.

Test of Imperceptibility: PSNR and SSIM
In order to show the differences between the original and watermarked images, the signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) are used [30]. The PSNR indicates the destruction rate while the SSIM is used to express the level of similarity ([31] [32]). These two metrics are used after embedding process.
Peak-Signal-To-Noise-Ratio (PSNR) is defining as follow: ( ) ( ) where I 2 is watermarked image and I 1 is original image. Bigger the PSNR is better the watermark conceals is [33].
The SSIM metric is defined by the following equation: σ x and σ y are the mean intensity of x and y. In the same time 2 x σ and 2 y σ are respectively variance of x and y [33]. σ xy is the covariance of x and y. The averages of x and y are μ y and μ x . Variables C 1 and C 2 are used to stabilize the division with weak denominator. The value of SSIM varies between −1 and 1, where the maximum value, i.e., 1 is obtained for two similar images [33].
Based on the results of this Table 1, it can be concluded that the destruction of images is acceptable after embedding process.

Robustness against Attacks
Bit Error Rate (BER) is one of many metrics use to verified the robustness of the proposed algorithm, we use it, in our case. It's calculated between original watermark and the extracted watermark after applying attacks on the watermarked images [33]. The bit error rate is calculated by: where W is the original watermark and EW is the extracted watermark. m and n are the size of the original watermark [34].

Comparison of Obtained Results
In this section we use many different types of attacks (like Gaussian), image processing attacks (resizing, rotation) and hybrid attacks (like salt & pepper and Gaussian filter)to demonstrate the robustness of the suggested watermarking algorithm on the watermarked images and then extracts the embedded watermarks. The average results of these tests are shown in Table 2. In the above table, focused of obtained results SSIM, NC and BER tests, we can conclude that the presented watermarking approach has better robustness against attacks in the embedding and the extracting processes of the proposed approach [35].
Tests results of our scheme are compare with the results of two other researchers scheme ([36] [37]), these results are better than the two others methods. Figure 3 and Table 3 show the results under different scale factor, the results of PSNR in our case are superior to 50 which denoted the robustness and the imperceptibility of the proposed scheme.
The difference and one advantage of our scheme is the use of audio logo which is transform in 2D then DCT transformed. This watermark is not easily recognizable.

Results of Obtained Watermarked and Encrypted Images
In this section, we present the obtained visual results after the conjoint phase of watermarking and encryption of the proposed algorithm. Figures 4-7 show that effectively the watermark is invisible and the encryption is realized. The two mains objectives for medical images security, imperceptibility and confidentiality are satisfied.

Security Analysis, Key Sensitivity Test
The secret key sensitivity is an essential characteristic for a good encryption-system; it guarantees the safety and robustness against exhaustive attacks.  The largest key space is very important, because of failure brute-force attacks.
Secret key for our proposed scheme is 3.93695629844, representing initial values of Logistic map, having 10 −11 precision [38]. When a change of 1 digit is made in the secret key, the result is very different in term of encrypted and decrypted image 2 [39]. Figures 8-11 show the results of key space analysis of our tests images.

Histogram Analysis
To get information about statistical properties of encrypted image, histogram analysis is a better way to obtain this information. Histogram of the encrypted image gives the distribution of pixels. Figure 12 shows the histograms of the original images used, and Figure 13 shows the histograms of these same encrypted images, where we note a uniform distribution, reflecting a good encryption.

Correlation Coefficient Analysis
Correlation analysis is very essential for the encryption phase and is carried out between the different pixel pairs of the original and encrypted images.
The correlation coefficients are calculated by the following formulas: where u and v are intensities values of two adjacent pixels, uv r is the correlation coefficient.
The pixels of an original image are strongly correlated in the horizontal,      vertical and diagonal directions. In order to know whether a cryptographic system should produce encrypted images without any correlation between adjacent pixels. Adjacent pixel correlation coefficients for horizontal, vertical and diagonal directions respectively, were calculated. Figure 14 shows the results of the horizontal correlation of the original image and Figure 15 shows the encrypted image.
It's remarkable in Figure 14.  Table 4. The values of correlation coefficients are very less under 1.
These give a conclusion that the encryption algorithm is very robust.

Speed Analysis
Speed of encryption and decryption is also use to characterize scheme. In our case the time results are obtained with computer having the following specifications Dell core Duo E7200 @2GHz, 1.96 GB RAM. Table 6 shows the time of encryption and decryption. This time varies depending on the image used.

Comparison Analysis
The calculation of the entropy is a statistical parameter of the image. It is given by the following formula:

Conclusion
We have proposed in this paper a method using chaos encryption based to solution of Vershult model combined with non-blind watermarking. This method consists of two mains phases; the first one is the non-blind watermarking associated with an audio signal. The second phase consists of encrypt watermarked image with logistic map knowing initials conditions, number of iterative conditions to generate chaos parameters. The results of PSNR, SSIM, NC, BER and correlation coefficients NPCR, UACI prove the imperceptibility and the robustness of your algorithm. Further research can be done in the following areas to improve the security of the medical images, as far as intelligent reversible watermarking is concerned. In the future, we intend to explore its ability to be robust against a specific attack through its learning mechanism. Reversible watermarking is also susceptible to different attacks in real watermarking applications.
We intend to incorporate single attack information in its learning mechanism first and later enhance it to a series of attacks. Another important aspect that could be taken into account is the security of the watermark itself. For this purpose, different encryption strategies, such as Petri reseau encryption, can be employed on the watermark before embedding. Further research could also focus on compressibility. When compression is applied after encryption, the randomness of the ciphertext will greatly reduce the amount of compression achieved.