- Research Article
- Open Access

# A Genetic Algorithm Optimization Technique for Multiwavelet-Based Digital Audio Watermarking

- Prayoth Kumsawat
^{1}Email author

**2010**:471842

https://doi.org/10.1155/2010/471842

© Prayoth Kumsawat. 2010

**Received:**15 February 2010**Accepted:**30 June 2010**Published:**8 August 2010

## Abstract

We propose a new approach for optimization in digital audio watermarking using genetic algorithm. The watermarks are embedded into the low frequency coefficients in discrete multiwavelet transform domain. The embedding technique is based on quantization process which does not require the original audio signal in the watermark extraction. We have developed an optimization technique using the genetic algorithm to search for four optimal quantization steps in order to improve both quality of watermarked audio and robustness of the watermark. In addition, we analyze the performance of the proposed algorithm in terms of signal-to-noise ratio, normalized correlation, and bit error rate. The experimental results show that the proposed scheme can achieve a good robustness against most of the attacks which were included in this study.

## Keywords

- Image Watermark
- Audio Signal
- Digital Watermark
- Quantization Step
- Watermark Embedding

## 1. Introduction

During the past few years, digital multimedia technology and Internet networks have made great progress and they are now becoming increasingly important in daily life. Consequently, intellectual property protection is a pressing concern for content owners who are exhibiting digital representation of the photographs, music, video, and original artworks through the Internet.

Digital watermarking is one of the most popular approaches considered as a tool for providing the copyright protection of digital contents. This technique is based on direct embedding of additional information data (called watermark) into the digital contents. Ideally, there must be no perceptible difference between the watermarked and original digital contents, and the watermark should be easily extractable, reliable, and robust against data compression or any signal manipulations [1]. The main requirements of digital watermarking are invisibility, robustness, and data capacity. These requirements are mutually conflicting, and thus, in the design of a watermarking system, the tradeoff has to be made.

According to the International Federation of the Phonographic Industry (IFPI) [2], audio watermarking should have the following specifications: audio watermarking should not degrade perception of original signal. signal-to-noise ratio (SNR) should be greater than 20 dB and there should be more than 20 bits-per-second (bps) data payload for watermark. watermark should be able to resist most common audio processing operations and attacks. watermark should be able to prevent unauthorized detection, removal, and embedding, unless the quality of audio becomes very poor.

In general, digital audio watermarking can be performed in time domain and transform domain, where the properties of the underlying domain can be exploited. Currently, watermarking techniques based on transform domain are more popular than those based on time domain since they provide higher audio quality and much more robust watermark.

Typical schemes for digital watermarking were based on transform-domain techniques with discrete cosine transform (DCT) [3, 4], discrete Fourier transform (DFT) [5, 6], and discrete wavelet transform (DWT) [7–12].

In recent years, some discrete multiwavelet transform-based digital watermarking algorithms have been proposed. Kwon and Tewfik [13] proposed an adaptive image watermarking scheme in the discrete multiwavelet transform (DMT) domain using successive subband quantization and a perceptual modeling.

Kumsawat et al. [14] proposed an image watermarking algorithm using the DMT and genetic algorithm (GA) applied to search for optimal watermarking parameters to improve the quality of the watermarked image and the robustness of the watermark. Ghouti and Bouridane [15] proposed a novel audio fingerprinting framework for robust perceptual hashing of audio content using balanced multiwavelets. In [16], Kumsawat et al. proposed a multiwavelet-based audio watermarking scheme by utilizing the audio statistics characteristics and quantization index modulation (QIM) technique.

Improvements in performance of digital audio watermarking schemes can be obtained by exploiting the characteristics of the human auditory system in watermarking process. It is possible to embed perceptually inaudible watermarks with more energy in an audio, which makes watermark more robust [12, 17].

Another way to improve the performance of watermarking schemes is to make use of artificial intelligence (AI) techniques. The watermarking system can be viewed as an optimization problem. Therefore, it can be solved by genetic algorithm [4, 14, 18], adaptive tabu search (ATS) [10], or support vector machine (SVM) [11]. There has been little research in application of GA to digital audio watermarking problems.

In this paper, we propose an audio watermarking method based on the discrete multiwavelet transform for the application of copyright protection. In our algorithm, the watermark is embedded into the multiwavelet transform coefficients using quantization index modulation technique. The watermark can be not only detected but also extracted to verify the owner. We apply the GA to search for four optimal watermarking parameters in order to achieve optimum performance. Finally, we have compared the experimental results before and after optimization using GA with the results of previous works.

This paper is organized as follows. In Sections 2.1 and 2.2, the preliminaries of multiwavelets and GA are introduced, respectively. Watermarking in the DMT domain with GA optimization is described in Section 3. In Section 4, the experimental results and discussions are shown. The conclusions of our study can be found in Section 5.

## 2. Preliminaries

### 2.1. Multiwavelet Transform

In recent years, multiwavelet transformation has gained a lot of attention in signal processing applications. The main motivation of using multiwavelet is that it is possible to construct multiwavelets that simultaneously possess desirable properties such as orthogonality, symmetry, and compact support with a given approximation order [14, 19]. These properties are not possible in any scalar wavelet (wavelet based on one scaling function). One of the well-known multiwavelets was constructed by Donovan, Geronimo, Hardin, and Massopust (DGHM) [20]. DGHM multiwavelets simultaneously possess orthogonality, compact support, an approximation order of 2, and symmetry.

Unlike scalar wavelet, even though the multiwavelet is designed to have approximation order the filter bank associated with the multiwavelet basis does not inherit this property. Furthermore, since the multiwavelets have more than one scaling function, the dilation equation becomes a dilation with matrix coefficients. Thus, in applications, one must associate a given discrete signal into a sequence of length vectors (where is the number of scaling functions) without losing some certain properties of the underlying multiwavelet. Such a process is referred to as prefiltering or multiwavelet initialization.

### 2.2. Genetic Algorithm

Genetic algorithm is one of the most widely used artificial intelligent techniques belonging to the area of evolutionary computation. Genetic algorithm based on the mechanisms of natural selection and genetics, has been developed since 1975 [21] and has been applied to a variety of optimization and search problems [4, 14, 18, 22]. GA has been proven to be very efficient and stable in searching for global optimum solutions. Usually, a simple GA is mainly composed of three operations: selection, genetic operation, and replacement. A brief summary for implementing GA can be summarized as follows.

## 3. The Proposed Watermarking Algorithm

In this section, we first give a brief overview of the watermark embedding and watermark extracting algorithms in the DMT domain based on the concept of the quantization index modulation technique. We then describe our proposed optimization technique in watermarking scheme using genetic algorithm.

### 3.1. Watermark Embedding Algorithm

The watermark embedding algorithm is described as follows:

Generate a seed by mapping a signature or text through a one-way deterministic function. The seed is used as the secret key ( ) for watermarking.

To increase security, perform a pseudorandom permutation in order to disperse the spatial relationship of the binary watermark pattern. Therefore, it would be difficult for a pirate to detect or remove the watermark. We use and to denote the original watermark image and the permuted watermark image, respectively. The relationship between and can be expressed as where is permuted to the pixel position in a secret order using the secret key Since the audio signal is one-dimensional, we should transform the permuted watermark image into the one-dimensional sequence in order to embed it in the audio signal. Then, the is transformed and mapped into a binary antipodal sequence for where is the length of watermark and

Transform the original audio signal using the DMT. Five-level DMT is chosen because it was found in our experimental results that the higher levels do not yield significantly better results while they increase computational complexity. Since the approximation coefficients are supposed to be relatively stable and less sensitive to slight changes of the audio signal, they are ideal embedding area. In order to achieve a balance between robustness and fidelity, the coefficients at coarsest approximation subband are selected for watermark embedding based on artificial intelligent technique. Furthermore, the coefficients in high-frequency subband are not used for watermark embedding because of their low signal energy in this frequency band.

Select the significant coefficients in the DMT domain which is the first largest coefficients at coarsest approximation subband to embed the watermark bits. The position of significant coefficients will be sent to the receiver as the side information.

Based on the statistical values of the selected coefficients, we have grouped them into 4 groups corresponding to their magnitudes. Each group will be quantizing with different quantization steps. To increase the watermarking security, we order the selected coefficients in a pseudorandom manner. The random numbers can be generated using the same secret key in generating the watermark

A large quantization step makes the watermark robust, but it will destroy the original quality of the audio signal. Thus, the value of quantization step should be as large as possible under the constraint of imperceptibility.

In order to optimize both quality of watermarked audio and robustness of the watermark, this work employs the genetic algorithm to search for 4 optimal quantization steps. These quantization steps are varied to achieve the most suitable watermarked audio signal for each given audio signal. The details of genetic algorithm optimization process will be described in details in Section 3.3.

### 3.2. Watermark Extracting Algorithm

The watermark extracting algorithm is outlined as follows:

Transform the watermarked audio signal into five-level decomposition using the DMT to obtain detailed coefficients and approximation coefficients. Then, we choose the first largest coefficients in the coarsest approximation subband from position in the side information and group them into 4 groups. We further order them in a pseudorandom manner using the secret key .

### 3.3. Improving Performance Using Genetic Algorithms

In the design of digital audio watermarking system, there are three goals that are always conflicted. These goals are imperceptibility, robustness, and data capacity. In order to minimize such conflicts, this work employs the genetic algorithm to search for 4 optimal watermarking parameters. This allows the system to achieve optimal performance for digital audio watermarking.

#### 3.3.1. Chromosome Encoding

Chromosomes in GA represent desired parameter to be searched. The population (chromosomes) size must be chosen carefully to give sufficient genetic diversity. A small-sized population reduces the evaluation cost but it may cause premature convergence. For a large-sized population, the higher computation time is required. Therefore, it is important to achieve a good or acceptable result within a reasonable computation time. In this paper, the proper population size is set to be 40 (as described in the next section). The encoding scheme is binary string with 32 bit resolutions for each chromosome. Hence, the parameter is represented by chromosome with length of 128 bits.

#### 3.3.2. Objective Function Evaluation

where and are weighting factors of and , respectively. These weighting factors represent the significance of each index used in GA searching process. If both indexes are equally significant, the values of these factors will be 0.5 each where the relationship must always hold. In this work, the weighting factors and are equally set to 0.5.

According to the International Federation of the Phonographic Industry, the of watermarked audio signal should be greater than 20 dB. Therefore, the value of desired has been assigned to 24 dB in all experiments. During GA-based optimization processes, three attacks are chosen to evaluate the robustness of the embedded watermark. They are MP3 compression at 64 kbps (Attack1), Gaussian noise addition (Attack2), and requantization (Attack3). Details of these attacks will be thoroughly described in Section 4.3. After obtaining the in the watermarked audio, the DIF value, and the average of the three normalized correlations after attacking, we are ready to start the objective function evaluation. An illustrative diagram is shown in Figure 6.

In order to gain the optimal performance of the quantization-based audio watermarking system, should be optimized at GA processes. By using objective function above, the parameter can be optimally searched to achieve the best of both output audio quality and watermark robustness.

#### 3.3.3. Selection, Genetic Operation, and Replacement

After evaluating fitness value of each chromosome based on the proposed objective function, chromosomes will be selected to produce offspring by crossover and mutation operations. In this work, a ranking selection is chosen for selection mechanism. The crossover is uniform, with probability of 0.7. Mutation is standard, with probability of 0.05. The chromosomes are then partially replaced by the best chromosome for each generation.

Parameters of genetic algorithm.

Parameters | Values |
---|---|

Population size | 40 |

Chromosome length | 128 |

Maximum number of generation | 30 |

Crossover rate | 0.7 |

Mutation rate | 0.05 |

## 4. Experimental Results and Discussions

In order to demonstrate the performance of the proposed algorithm, some numerical experiments are carried out to measure the audio quality of the watermarked audio and evaluate the robustness of the watermark under typical attacks.

where and denote the original and modified audio, respectively.

### 4.1. Results of Genetic Algorithm Optimization

Average results for different population sizes.

Population sizes | |||||
---|---|---|---|---|---|

Attack1 | Attack2 | Attack3 | |||

10 | Average | 0.999960 | 0.999970 | 0.999960 | 3.111 |

Stdev | 0.000084 | 0.000483 | 0.000069 | ||

20 | Average | 0.999980 | 0.999970 | 0.999970 | 3.308 |

Stdev | 0.000632 | 0.000674 | 0.000048 | ||

30 | Average | 0.999998 | 0.999960 | 0.999950 | 3.316 |

Stdev | 0.000031 | 0.000843 | 0.000084 | ||

40 | Average | 0.999998 | 0.999998 | 0.999998 | 3.362 |

Stdev | 0.000031 | 0.000004 | 0.0000042 | ||

50 | Average | 0.999960 | 0.999998 | 0.999998 | 3.368 |

Stdev | 0.000484 | 0.000031 | 0.000004 |

Quantization steps from GA optimization of 10 test audios.

Host signal | Quantization step | |||
---|---|---|---|---|

Classical1 | 0.3654 | 0.3309 | 0.3905 | 0.3497 |

Classical2 | 0.3482 | 0.3391 | 0.3100 | 0.3196 |

Country1 | 0.3311 | 0.3402 | 0.3005 | 0.3215 |

Country2 | 0.3425 | 0.3308 | 0.3772 | 0.3211 |

Jazz1 | 0.3482 | 0.3398 | 0.3074 | 0.3024 |

Jazz2 | 0.3311 | 0.3960 | 0.3022 | 0.3084 |

Rock1 | 0.3340 | 0.3391 | 0.3008 | 0.3200 |

Rock2 | 0.3426 | 0.3342 | 0.3313 | 0.3115 |

Pop1 | 0.3311 | 0.3952 | 0.3005 | 0.3091 |

Pop2 | 0.3473 | 0.3477 | 0.3015 | 0.3194 |

### 4.2. Imperceptibility Test Results

The watermarked audio quality is examined by watermarking the original audio signals with the resulting parameters from GA. Then, the SNR test is conducted, which serves as an objective measurement of audio signal quality. The SNR is measured by comparing the watermarked signal with the original one.

Signal-to-noise ratio of watermarked audio signals.

Host signals | SNR (dB) | |
---|---|---|

Without-GA | With-GA | |

Classical1 | 25.31 | 26.04 |

Classical2 | 22.23 | 23.85 |

Country1 | 28.60 | 30.30 |

Country2 | 23.06 | 24.91 |

Jazz1 | 23.03 | 27.97 |

Jazz2 | 26.09 | 27.67 |

Rock1 | 26.73 | 28.30 |

Rock2 | 27.99 | 29.36 |

Pop1 | 21.82 | 24.90 |

Pop2 | 22.12 | 24.67 |

Average | 24.69 | 26.79 |

### 4.3. Robustness Test Results

We first tested the robustness of the proposed algorithm to ten audio samples under no attacks. If the BER of the recovered watermark sequence is 0, it means that the embedded bit can be recovered exactly. The effects of the following eight types of attacks are then investigated.

Resampling: the audio signal is first downsampled at 22.05 kHz, and then upsampled at 44.1 kHz.

Requantization: the 16-bit watermarked audio signals have been requantized down to 8 bits/sample and back to 16 bits/sample.

Low-pass filtering: low-pass filtering using a second-order Butterworth filter with cutoff frequency of 6 kHz, 12 dB/octave roll-off, is performed to the watermarked audio signals.

Addition of noise: white Gaussian noise with 1% of the power of the audio signal is added.

Cropping: two thousand samples of each testing signal are cropped out at 5 random positions.

Low bitrate codec: the robustness against the low-rate codec was tested by using MPEG 1 Layer III compression (MP3) with compression rates of 56, 64, 96, and 128 kbps.

Digital-to-analog/analog-to-digital (DA/AD) with same rate reacquisition: the output of audio signal from a sound card is connected to the analog input of another computer.

Time-scale modification (TSM): time-scale modification between +5% and of the total audio excerpt length is performed.

Robustness comparison of our algorithm (average values).

Attack type | Without-GA | With-GA | ||
---|---|---|---|---|

NC | BER (%) | NC | BER (%) | |

Attack free | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

Re-sampling | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

Requantization | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

Low-pass filtering | 0.9292 | 8.0133 | 0.9393 | 6.9336 |

Additive noise | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

Cropping | 0.9031 | 5.2636 | 0.9983 | 0.1953 |

MP3-56 kpbs | 0.9992 | 0.0977 | 0.9992 | 0.0977 |

MP3-64 kpbs | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

MP3-96 kpbs | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

MP3-128 kpbs | 1.0000 | 0.0000 | 1.0000 | 0.0000 |

DA/AD | 0.8486 | 17.2852 | 0.9488 | 5.7617 |

0.8970 | 11.8164 | 0.9805 | 2.2461 | |

0.8660 | 16.0616 | 0.9814 | 2.1484 |

For low-pass filtering, cropping, MP3 compression at 56 kbps, DA/AD, and TSM attacks, the BER values of the recovered watermark sequence are 8.0133%, 5.2636%, 0.0977%, 17.2852%, 11.8164%, and 16.0616% for the Without-GA method and 6.9336%, 0.1953%, 0.0977%, 5.7619%, 2.2461%, and 2.1484% for the with-GA method, respectively. Although a lot of loss occurred in the audio signal, the bit error rates are still acceptable. The results show that our proposed method yields better results than the method without-GA. Because GA search guarantees the global optimum solution, the proposed method can thus improve the quality of the watermarked audio and give almost the same robustness of the watermark.

Algorithm comparison.

Algorithm comparison.

Attack free | Re-sampling | Requantization | Low-pass filtering | Additive noise | |
---|---|---|---|---|---|

[10] | |||||

BER (%) | 0 | 0 | 0.1953 | 3.3203 | 2.6367 |

SNR (dB) | 24.1209 | 23.5533 | 20.0936 | 10.3506 | 19.5607 |

With-GA | |||||

BER (%) | 0 | 0 | 0 | 1.1719 | 0 |

SNR (dB) | 24.5518 | 23.5052 | 20.9320 | 10.3884 | 19.5684 |

Cropping | MP3 128 kbps | MP3 96 kbps | MP3 64 kbps | MP3 56 kbps | |

[10] | |||||

BER (%) | 5.3711 | 3.6133 | 4.1016 | 5.3711 | 5.7617 |

SNR (dB) | 10.8289 | 19.5607 | 19.5537 | 18.5348 | 18.5400 |

With-GA BER (%) SNR (dB) | |||||

0.1953 | 0 | 0 | 0 | 0 | |

16.3075 | 19.7552 | 19.5920 | 18.8265 | 18.6666 |

Table 7 shows test results of Rock1 audio signal with no attack, re-sampling, requantization, low-pass filtering, addition of noise, cropping, and MPEG 1 Layer III compression with compression rates of 128, 96, 64 kbps and 56 kbps, respectively. The BER of watermark signal and the SNR of digital audio signal are also displayed.

According to these results, the extracted watermark images from our proposed method have some distortion for low-pass filtering and cropping attacks but they are still visually recognizable. In addition, the bit error rates of the extracted watermarks using our proposed method are always lower than the ones using method in [10]. The results demonstrate that our proposed method yields significantly more robust watermark than the method in [10] does.

## 5. Conclusions

This paper proposes a digital audio watermarking algorithm in the multiwavelet transform domain. In order to make the watermarked signal inaudible, the watermark is embedded into low frequency part of the highest energy of audio signal by taking advantage of multiresolution characteristic of multiwavelet transform. The watermark insertion and watermark extraction are based on the quantization index modulation technique and the watermark extraction algorithm does not need the original audio in the extraction process. Performance improvement with respect to existing algorithms is obtained by genetic algorithm optimization. In our optimization process, we use genetic algorithm searching for optimal parameter which is the quantization step. This parameter is optimally varied to achieve the most suitable for original audios with different characteristics. The testing results of the watermarked audio quality and watermark robustness with various watermark attacks show that our proposed method can improve the performance of the watermarking process such that the better watermarked audio quality and watermark robustness are achieved. Further research can be concentrated on the development of our proposed method by using the characteristics of the human auditory system and psychoacoustic model.

## Declarations

### Acknowledgments

This paper was supported by a grant from Suranaree University of Technology, Thailand Research Fund and Commission on Higher Education. The author would like to thank anonymous reviewers for their comments and suggestions which have improved the readability and technical content of this paper.

## Authors’ Affiliations

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