Robust Audio Watermarking based on HWD and SVD

Draft: submitted to 20th Iranian Conference on Electrical Engineering, 2012. Robust Audio Watermarking Based on HWD and SVD Saeed Karimimehr*, Shadrokh Samavi**, Hoda Rezaee Kaviani***, Mojtaba Mahdavi**** *Isfahan University Of Technology, Isfahan, Iran, [email protected] **Isfahan University Of Technology, Isfahan, Iran, [email protected] ***Isfahan University Of Technology, Isfahan, Iran, [email protected] ****Isfahan University Of Technology, Isfahan, Iran, [email protected] Abstract: To protect copyright of audio signals several watermarking algorithms have been proposed in recent years. Many of them are based on wavelet transform but these methods are not robust enough against signal processing attacks. This paper presents a new audio watermarking algorithm based on Hybrid wavelets and Directional Filter banks (HWD) and Singular Value Decomposition (SVD). The proposed method embeds the watermark in the directional subbands of audio matrix. To do multiple embedding, framing is used and each frame is split to two parts. The first one is used for the synchronization code and the other for watermark embedding. Synchronization code is embedded in time domain to achieve more efficiency and watermark is embedded in SVDblocks of different directions using HWD. Experimental results show that proposed method has increased robustness and imperceptibility. It also has an acceptable data payload. Keywords: Audio Watermarking, Hybrid Wavelets and Directional Filter banks, SVD. 1. Introduction Due to growth of Internet and computer networks, digital multimedia contents can easily be exchanged among people. This ease of distribution and accuracy of these methods to duplicate a multimedia in an inexpensive way caused tough challenges to copyright protection and intellectual property. A response to this problem is digital watermarking [1] which includes three main categories: image, audio and video watermarking. Although audio and image watermarking are similar in some aspects but there are more complications in audio watermarking. For example the Human Auditory System (HAS) is much more sensitive to changes than the Human Visual System (HVS). The other challenge is that, the ratio of the highest to the lowest audible frequency is approximately 1,000 (range of 20Hz-20 kHz) where this ratio for light waves we can see is a factor of 2 [2]. Opposite to its large dynamic range, HAS contains a fairly small differential range, i.e. loud sounds generally tend to mask out weaker sounds [3]. According to IFPI (International Federation of the Phonographic Industry), an audio watermarking must have some minimum properties: (1) A watermarked audio signal should maintain more than 20 dB SNR. (2) Watermarked signals should not reveal any clues about the watermarks in them. Also, the security of the watermarking procedure must depend on secret keys, but not on the secrecy of the watermarking algorithm. (3) A watermarking scheme must have the ability to extract the watermark from a watermarked audio signal after applying various signal processing attacks. (4) The amount of data that can be embedded into the host audio signal without losing imperceptibility (Payload) should be more than 20 bps. There are mainly two types of attacks which may distort a watermarked audio: (1) Modifying the amplitude of audio signal which results in the lost of parts of hided information. These attacks include noise corruption, amplitude scaling, re-sampling, and MP3 compression. (2) Destroying synchronization of the watermark in time domain that is more effective than corrupting watermarked audio amplitude directly and includes attacks such as time scaling, shifting and cropping. There are few methods which withstand against synchronization attacks. A lot of audio watermarking schemes based on the WT (Wavelet Transform) have been introduced [4] in recent years. To overcome some of the restrictions of the WT, in [5, 6] authors introduced the lifting scheme of wavelets for the first time. An algorithm based on LWT (Lifting Wavelet Transform) is proposed by [7], which has showed that watermark detection can be implemented quickly without presence of the original signal, but the method is not very robust. Another improved algorithm presented by [8] proposes a method of quantization that is more robust. One of the main problems that most of the methods had was their weakness against synchronization attacks. It means that for example once the position was lost by random cropping, the proper watermark cannot be detected easily. The method in [9] uses a synchronization signal in embedding procedure and in extraction phase, the detection begins after the synchronization signal is located. Although this method can resist some random cropping attacks, the watermark still cannot be extracted properly if the watermarked signal is cut. In [10] a lifting wavelet domain audio watermarking algorithm based on the statistical characteristics of sub-band coefficients is proposed. This method uses self synchronization but since it embeds the synchronization code in wavelet domain, the detection procedure is very time consuming. Altogether its robustness is not so good. After representing directional transforms, it has been shown [11, 12] that they are more efficient than wavelet in representing a two dimensional signal. It means that they capture significant information about an object of interest using a small description. In this paper a self synchronization method is presented which embeds a synchronization code in each frame of the original audio signal. The watermark is a binary logo which is embedded in SVD-blocks of different directional subbands of HWD transform. HWD Draft: submitted to 20th Iranian Conference on Electrical Engineering, 2012. transform is a new family of non-redundant multiresolution directional transforms presented by Eslami et al. [12]. In proposed method watermark is encrypted using Arnold map before embedding to prevent unauthorized detection. We call our method as Robust HWD based Algorithm (RoHA). Experimental results are compared with [10] and show high performance of proposed algorithm. The rest of the paper is organized as follows: Section 2 explains the proposed audio watermarking approach. Section 3 gives the experimental results and evaluations and Section 4 gives some concluding remarks. 2. Proposed Method In this section we intend to present the details of proposed algorithm but first we need some explanation of the chaotic encryption algorithm. Then Hybrid Wavelets and Directional Filter banks are briefly introduced. We also offer a short discussion on singular value decomposition. Then the embedding and extraction procedures are explained. 2.1 Chaotic Encryption Algorithm Chaotic maps are used to encrypt watermarks. In the literature of watermarking, chaotic maps prevent unauthorized detection. Here we use the Arnold transform, since the Arnold transform is periodic, the number of scrambling can be considered as the key to enhance the security. The Arnold transform for an N by N matrix is shown below. ′ ′ 1 1 (1) ( ) 1 2 where (x, y) is the pixel of the watermarking image and (x ′ , y′) is the pixel of the watermarking image after scrambling. 2.2 = Hybrid Wavelets and Directional Filter banks In [12] Eslami proposed a family of non redundant transforms using Hybrid Wavelets and Directional Filter banks. They extended the directionality of the wavelet transform by employing the DFBs to the high pass channels of the wavelet transform. Therefore, they used the name hybrid wavelets and directional filter banks (HWD) transform family. Since, in the WT, we already have horizontal and vertical sub bands, different paradigms could be considered to apply DFBs to the finest subbands of wavelets. They proposed two types of HWD transforms. Here we use HWD-F. Fig. 1: Schematic plot of HWD-F transform for = 3 directional levels. To achieve HWD-F we apply full-tree DFBs with l j levels to all three highpass subbands of wavelets at levels1 . We denote the subbands by ( ) () () , and (2) ( ∈ ( ) = { |1 (3) 2 }) A schematic diagram of the HWD-F transform is illustrated in Fig. 1. Using the noble identities [13], we can move the DFB filters before down sampling by in the WT. It is notable that we can use any number of directions in DFB stage and both stages, WT and HWD, are nonredundant. Consequently, the HWD transforms provide a family of non-redundant and flexible basis elements. 2.3 Singular Value Decomposition The singular value decomposition of a matrix is a factorization of the matrix into a product of three matrices. Given an × matrix A, where , the ′ SVD of A is defined as = . Where is a × column orthogonal matrix whose columns are referred to as left singular vectors: = ��(�1 , �2 , … , � ) is a × matrix whose diagonal elements are nonnegative singular values arranged in descending order: is an × orthogonal matrix whose columns are referred to as right singular vectors. If � = , then satisfies: �1 �2 ⋯ � � +1 = � = 0 (4) According to [14] the singular values (SVs) of a matrix have very good stability, that is, when a small perturbation is added to a matrix, its SVs do not change significantly and SVs represent intrinsic algebraic properties of a matrix. 2.4 Embedding Process of RoHA In our method first we use framing in order to increase robustness against synchronization attacks. Each frame consists of two parts as depicted in Fig. 2. Segment i Synchronization Code Watermark W(i) Fig. 2 Construction of each frame Draft: submitted to 20th Iranian Conference on Electrical Engineering, 2012. (4) Matrix formation: After finding the lowest frequency, the achieved one dimensional vector is reshaped to a two dimensional matrix (matrix formation). (5) Hybrid Wavelets and Directional Filter bank: Here the output of wavelet is passed from the HWD block, According to section 2.2. Then for each subband (H2, V2, D2), 2 submatrices are driven, each one shows one direction in corresponding subband. It means that there are = 3 × 2 matrices ( ) in output of block #5. (6) Embedding: In the embedding process each vector is embedded in its corresponding matrix. To do so, each bit of vector is embedded in each block of corresponding matrix as following steps: Step1: Partition the matrix into 2D matrix blocks , = 1,2, … , × , each of size × , where × is the number of bits in the corresponding vector . The row and column numbers of 2D blocks are selected by the user to achieve proper imperceptibility as well as robustness and the SVD of each block is computed. Step2: Let � = (�1 , �2 , … , � ) be the vector of SVs of block . The norm of this vector is computed as follows: = � Fig. 3.Watermark embedding flowchart for each frame After framing we do the same thing with all of the frames as shown in the block diagram of Fig. 3. Note that the length of each segment depends on the data payload that we would like to embed. The larger the frame is, the more data can be embedded. For synchronization code embedding we used the same method used in [15] which is in the time domain. Hence, searching for the synchronization code is performed faster than transform domain methods. The description of blocks in Fig. 3 for embedding the watermark is as follows: (1) Watermark logo: is a × binary image. (2) Watermark encryption: In order to prevent unauthorized detection we used encryption as explained in section 2.1. The outcome of the encryption block ( ) is broken into = 3 × 2 row vectors. In this equation, 3 stands for number of wavelet subbands that are vertical, horizontal and diagonal in HWD and 2 is the number of directions used in DFB stage of HWD. (3) Wavelet filter: To best merge the watermark and the signal it is better to embed the watermark in the most significant part of the signal. Here we used two levels of DWT to reach to the lowest subband where there is concentration of most energy. = =1 (� (5) )2 Step3: Compute the mean ( ) and standard deviation (� ) for each block. Step4: The weight of each block is given by: = + ×� (6) � × In equation (6) parameters of and are user � defined parameters. Step5: Amongst all values, the maximum and the minimum are chosen and called and respectively. Step6: To increase robustness and decrease distortion, we propose adaptive decision method for quantization steps, which is better than using constant steps. The quantization step ∆ for block is calculated adaptively using equation (7): ∆ =∆ + ∆ −∆ − , = 1,2, … , − × (7) In this equation ∆ and ∆ are user-defined minimum and maximum quantization step values, respectively. Step7: Then the integer the quantization step for . Step8: Each bit ( , ) of embedded as follows: If ( , =1� If ( , =0� Step9: Calculate the value of SVs as follows: �1 , �2 , … , � = ∆ is computed, where ∆ is , Corresponding to the block the watermark sub segment is 2 = 1), then = + 1 2 = 1), then = + 1 ∆ ′ = ∆ × + and the value = (�1 , �2 , … , � ) × 2 ′ (8) Step10: The watermarked blocks are obtained by applying the inverse SVD using the modified SVs. Then Draft: submitted to 20th Iranian Conference on Electrical Engineering, 2012. the matrices blocks. ′ are reconstructed from all the modified 2.5 RoHA Extraction Process Generally, we should avoid false synchronization during selecting synchronization code. Several reasons contribute to false synchronization: 1) the style of the synchronization code, 2) the length of synchronization code, 3) the probability of "0" and "1" in synchronization code. Amongst all of them, the length of the synchronization code is especially important. The longer it is, the more robust it is. Most of the times, synchronization code is embedded in spatial domain in order to have fast access. But embedding in spatial domain often causes much distortion to cover. The same as embedding process, synchronization code extraction is driven from [15] which is a simple and direct method. A correlation measure is used to compare both bit sequences. The watermark can be extracted without using the original audio signal as follows: Step1: Locate the beginning position of the watermark in the audio frame using synchronization code searching technique as explained in [15]. The output is a vector with a pre-specified length given as a secret key. Step2: Apply two levels of DWT to reach to the LL subband. Then reshape the LL subband into a matrix. Step3: Apply HWD with 2 direction (k is the number of directions in embedding phase). Now find watermark bits from 3 × 2 matrices as follows: Partition each matrix into 2D matrix blocks of size × . For each block compute the value = � where the vector � = �1 , �2 , … , � is formed by the SVs of the block. Find the integer = ∆ . If 2 = 0, then the embedded bit is 1, otherwise it is 0 (Value of ∆ is provided by the embedder as a secret key). Then put the bits in sequence to achieve the watermark vector and reshape the achieved vector. 3. For the robustness test we have done two groups of attacks: attacks that modify the amplitude of the signal and attacks that de-synchronize the watermarked signal. 1) First group: (1) Lowpass filtering1, 2: application of a 9th-order Chebyshev filter with a cut-off frequency of 11.025,8 kHz; (2) Noise adding: addition of zero-mean white noise which variance is 0.01; (3) Re-quantization: re-quantization from 16-bit to 8bit and then back to 16-bit; (4) Re-sampling: down-sampling to 22.05 kHz followed by up-sampling back to 44.1 kHz; (5) MP3 Compression: compression of the audio signal with a compression rate of 22:1, then decompression of the signal. 2) Second group: (1) Ten percent of the audio signal is cropped at one of three selected positions randomly (front, middle and back); (2) Jittering: cropping of one sample out of every 100, 500, 1000, 2000 samples; (3) Random cropping 1: selection of 5 positions randomly and removal of 100 samples at each position; (4) Random cropping 2: selection of 10 positions randomly and removal of 100 samples at each position; (5) Random cropping 3: selection of 10 positions randomly and removal of 500 samples at each position; (6) Random cropping 4: selection of 10 positions randomly and removal of 1000 samples at each position. Table I is a reference that shows the relation between the Bit Error Rate (BER) and visibility of binary watermark logo. Bit Error Rate (BER) is used to evaluate the watermark detection accuracy after signal processing operations. The BER of the watermarked signal retrieval is defined as follows: , Experimental Results To evaluate our scheme, we carried out performance and robustness tests and compared the watermark detection results with that of reference [10]. All of the audio signals in the test were music clips recorded at 16 bits per sample and 44.1 kHz. We used a 32 × 24 binary image as our watermark logo. For all audio signals a 16bit Barker code of 1111100110101110 for synchronization is used. We fixed the length of each embedded watermark segment at 262,320 samples. In the HWD stage we used 8 directions to embed. Our block sizes for SVD were 8 by 8. The other parameters were = 11 (this parameter is used in the synchronization step [16]), = 0.05, ∆ = 0.48 and � = 0.80, ∆ = 0.50. All of the parameters were found to achieve the best trade-off between robustness and imperceptibility. = =1 ( , )⨁ ( , ) × =1 (9) In Equation (9) and are the original and the extracted watermarks respectively. Also, and are watermark’s width and length and ⨁ represents the exclusive OR (XOR) operator. To evaluate the similarity between the original and the extracted watermarks Normalized cross-Correlation (NC) is computed using Equation (10): , =1 = =1 =1 =1 2 , , (, ) =1 =1 2( , ) (10) All of the parameters used in Equation (10) are previously defined. Draft: submitted to 20th Iranian Conference on Electrical Engineering, 2012. Table II shows the results after applying several attacks on watermarked signals in comparison with [10]. As it is shown, the proposed RoHA method is more robust than the scheme in [10]. The quantization step for embedding, the barker code for synchronization and the encryption of the watermark before embedding are the main security parameters in our method. As we embedded the synchronization code in time domain, detection process in our method is faster than scheme of [10] because this scheme embeds the synchronization code in wavelet domain which is time consuming to extract. TABLE I: The relation between the BER and visibility of binary watermark image BER (%) 0 5 10 Binary watermark image BER (%) 20 25 Binary watermark image TABLE II: Extracted watermark by proposed scheme Ref [10] NC Proposed NC Proposed BER (%) 1 1 0.986 Ref. [10] BER (%) 0 0 0 No attack Lowpass filter:1 Lowpass filter:2 1 1 1 Noise addition Re-quantization Re-sampling MP3 compression 1 1 1 0.981 1 1 1 0.922 0 0 0 1.95 0 0 0 7.8 Add 10% (front) Add 10% (middle) 1 1 1 1 0 0 0 0 Cropping 10% (front) 1 1 0 0 Cropping 10% (middle) 1 1 0 0 Jittering:1 Jittering:2 Jittering:3 Jittering:4 0.802 0.923 0.965 0.975 1 1 1 1 19.79 7.81 3.51 2.60 0 0 0 0 0.997 1 0.26 0 0.957 1 4.29 0 0.905 1 9.50 0 0.901 0.992 10.28 0.78 Random cropping:1 Random cropping:2 Random cropping:3 Random cropping:4 Conclusion References 15 Attack type 3. In this paper we proposed a new robust digital audio watermarking algorithm which uses framing in order to embed multiple copies of a watermark to achieve higher robustness. To perform embedding each frame is split into two parts of synchronization code and watermark parts. Each bit of synchronization code is embedded in a sequence of samples in time domain. 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