In the modern days, watermarking has wide applications as per the security concern of digital content. The digital content is available in the form of image, audio, and video. The watermarking in digital content is called digital watermarking. Digital watermarking is a process of hiding a message similar to digital content within the signal itself. Digital watermarking can be proposed for multiple purposes like copyright protection, source tracking and hidden communication.
In this thesis, a digital audio watermarking scheme is developed, addressing the issue of copyright protection. The watermarking algorithm is developed by the combination of a discrete wavelet transform (DWT) and singular value decomposition (SVD) framework. We implemented a Bacterial Foraging Optimization (BFO) algorithm to the DWT-SVD watermarking algorithm. The DWT-SVD-BFO watermarking algorithm is provided better copyright protection to the digital audio content. All the scripts are generated in the MATLAB software.
Figure 1 spectrum of the original audio signal, DWT-SVD watermarked audio signal, and DWT-SVD-BFO watermarked audio signal
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Following characteristics of digital watermarking are mentioned below;
- Computational efficiency
Some applications of digital watermarking are given below;
- Broadcast monitoring
- Copyright protection
- Content authentication
- Owner identification
- Copy control
We proposed an audio watermarking algorithm for the protection of the audio signal from theft and tempering. We used the combination of Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) with Bacterial Foraging Optimization (BFO) optimal tuning for embedding a signal into the actual audio signal. The formulation of embedding single is
In equation 1, Sw shows watermarked audio signal; S reflect the actual audio signal and W is the message bit of watermark signal. Here alpha (a) reflects the gain factor based on the estimation of robustness and imperceptibility of the message signal. The gain factor is the deciding element of the watermarking process. The optimal value of the gain factor is selected via the BFO algorithm. The optimal gain factor is improved the PSNR (Peak Signal to Noise Ratio) and minimises the MSE (Mean Square Error).
Figure 2 Block diagram of watermark embedding
Figure 2 shows the block diagram of the watermark embedding system of an audio signal. The input is an audio signal which transforms in the frequency spectrum using DWT. The key function of the DWT is transforming the audio signal into the time-frequency spectrum. A four-level DWT decomposition of the audio signal is performed for the watermarking. A matrix is formed based on the DWT transformation. The DWT matrix is modified via the SVD operator. The SVD operator embedded a watermark on the off-diagonal zero elements of the DWT matrix. The singular value of the DWT matrix remains unchanged. The gain value of the SVD is tuned via the BFO algorithm.
Steps of Watermark embedding
- Convert the binary image of the watermark into the single-dimensional vector of size M*N.
- The real audio signal is converted into the sampled file, which further divided into N frames.
- The four levels of DWT decomposition is performed on each frame. In this stage five multi-resolution sub-bands produced. Among five sub-bands four are detailed sub-bands and one is approximation sub-band.
- Formulate a matrix D based on the four detailed sub-bands. The watermark bits distributed to the matrix in a multi-resolution manner.
- Applied SVD operator to the generated matrix D which produces three orthonormal matrices Σ, U, and VT as
D =U *Σ* VT
Σ matrix has the same size 4 × 4 as contains by D. This matrix is used for the watermarking process and denoted by S
- Arrange 12 bits of the original watermark bit vector b into a scaled 4 × 4 watermark matrix W. The watermark bits must be located in the non-diagonal positions within the matrix, as shown below
- The BFO algorithm is applied to select the optimal gain factor value The steps of BFO studied in the next section.
- We have embedded the watermark matrix W into the matrix S as shown in equation 1 above. A watermark matrix is obtained in this step.
- The new generated watermark matrix Sw is decomposed by the SVD operator, which formulate three new matrices. The matrices U1 and V1T are stored for later use in the extraction process
SW = U1 * S1 * V1T
- Apply the inverse SVD operation using the U and V matrices, which were unchanged, and the S1 matrix, which has been modified according to Equation below. The Dw matrix given below is the watermarked D matrix.
Dw =U *Σ’* VT
where matrix Σ′ is the original Σ matrix with the S sub-matrix replaced by the S1 sub-matrix.
- Apply the inverse DWT operation on the Dw matrix to obtain the watermarked audio frame.
- Repeat all previous steps on each frame. The overall watermarked audio signal is obtained by concatenating the watermarked frames obtained in the previous steps
Operation of BFO algorithm
The objective function for the proposed embedding system is formulated and should be minimized.
Figure 3 BFO operations step by step
For each selection of gain values, the embedding algorithm is executed, and fitness value is calculated by above equation 2. Once all iterations are finished, the gain factor values for minimum fitness function are picked as the final gain values. These values are used further for the embedding of the watermark message.
Retrieval of Watermark
Figure 4 Retrieval of Watermark
Figure 4 reflects the retrieval process of watermark audio signal. From the watermarked audio signal two matrices are U1 and V1 computed for each frame. The original audio signal can be separated from the watermarked signal as shown in figure 4. The steps of watermarked message retrieval explained below;
- Figure out the matrix S1’ for each frame of the watermarked audio signal.
- Multiply matrix S1′ by U1 and V1, which were computed in the watermark embedding procedure and stored for use in the extraction process. This results in the following matrix.
- Extract the 12 watermark bits from each frame by examining the non-diagonal values of matrix Sw’. W(n) is extracted according to the following formula:
4. Construct the original watermark image by assembling the bits extracted from all frames.
Results and Discussion
The proposed work is implemented in the MATLAB software with the signal processing toolbox. MATLAB’s signal processing toolbox provided may functions ready to use, which reduces our hassle to write a script for those, and we were able to concentrate on our proposed work’s implementation. The results have been tested for a recorded signal at 44100 Hz frequency as well as a live recording of an audio signal at the same frequency. The analysis is performed based on the different sizes of watermarked message signals.
The actual audio signal is divided into the 50 chunks. The number of tuning variables is equal to the chunks in BFO. The different gain factors are used for the 50 different chunks. So 50 gain values are available for each chunk instead of DWT-SVD embedding scheme. An output comparison of NCC, PSNR and MSE is shown in figure 5 (a), (b) and (c) respectively.
Figure 5(a): NCC comparison of DWT-SVD and DWT-SVD-BFO (b) PSNR Comparison (c) MSE Comparison
Figure 6: Bar plot comparison of DWT-SVD and DWT-SVD-BFO method
Figure 7 % improvement plot by proposed scheme for live recorded audio signal
In this work, we proposed a new algorithm BFO for the tuning of a gain factor of embedding a watermark message into the audio signal. The audio signal is decomposed via DWT-SVD method then BFO applied. The performance of the proposed method is evaluated based on PSNR, NC and MSE parameters.
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