CN102664014B - Blind audio watermark implementing method based on logarithmic quantization index modulation - Google Patents

Abstract

A method for implementing blind audio watermarking based on logarithmic index modulation belongs to the technical field of audio watermarking, and is characterized in that the robustness of vector norm and the imperceptibility of logarithmic index modulation based on mu-law companding are fully utilized , and use the chaotic sequence to encrypt the watermark image to improve the security and robustness of the watermark, convert the vector norm of the segmented wavelet approximate component to the transform domain through mu-law companding, and then embed the encrypted binary watermark image, after After the watermarking attack, the binary watermarked image is extracted. The audio watermarking algorithm proposed by the present invention not only has the characteristics of high capacity and good sound quality, but also has the advantages of good imperceptibility, good robustness, and low complexity. In the case of various watermark attacks, this method can still be used The watermark is correctly extracted, and this method can effectively resist amplitude attacks.

Description

A Blind Audio Watermarking Method Based on Log Quantization Index Modulation

technical field

The invention relates to a blind audio watermark implementation method based on logarithmic index modulation. The method not only has the characteristics of high capacity and good sound quality, but also has the advantages of good imperceptibility, good robustness and low complexity. In the case of various watermark attacks, the method can still be used to extract the watermark correctly, and this method can effectively resist the amplitude attack.

Background technique

Digital watermarking (Digital Watermarking) is to use the redundancy of human perception system (such as visual or auditory system) to embed some identification information in image, audio and other carriers, but it does not affect the use value of the original carrier.

According to different watermarking carriers, watermarking technology can be divided into video watermarking, image watermarking, audio watermarking and so on. At present, video and image watermarking technology has been developed relatively maturely. Due to the following reasons, audio watermarking has gradually become the focus and hotspot of watermarking research: first, audio is widely used and is an important tool for human communication; second, there are a lot of redundant audio in audio. In addition, it is convenient to embed watermark information. However, audio watermarking is very different from image watermarking, mainly because: 1. Audio is a one-dimensional signal; Visual is more difficult; 3. The volume of audio data is large, and it is mainly used in broadcasting, online distribution and other environments. It is very difficult to find the original audio. Therefore, in principle, the detection and extraction of watermarks should not require the original audio, that is, to achieve blind detection.

In general, audio watermarking should meet the following basic requirements: (1) imperceptibility: refers to the degree to which the original audio quality is affected after the watermark is added; (2) robustness: refers to the watermarked audio can resist various (3) capacity: refers to the number of watermarks embedded in the original audio per second; (4) complexity: refers to the time and space complexity of the algorithm. Usually the above requirements are contradictory, so we often choose a balance according to the needs of practical applications.

One of the currently used audio watermarking methods is: audio watermarking based on spread spectrum. The main advantages are: it can improve the anti-interference ability of the signal in the case of low-power transmission, and has high concealment. Even if the signal of several frequency bands is lost, the signal can still be recovered, and it is guaranteed that only the receiver with the known spread function can detect the signal. Implement blind detection. The main disadvantages are: too much spectrum is occupied, and the amount of embedding is small; the premise of blind detection is that the watermarked audio signal and the watermarked random signal must be completely synchronized. In order to get a smaller watermark extraction rate, the watermark length must be large enough, but this will increase the detection complexity and delay.

The second audio watermarking method currently used is: audio watermarking based on quantization index modulation. The main advantages are: simple algorithm, low complexity, large amount of embedded information, easy blind extraction, imperceptibility, and a balance between robustness and capacity. The main disadvantage is that it is sensitive to noise, and the algorithm uses a fixed quantization step size, which introduces a large quantization noise, so the extraction error caused by the data fluctuation caused by quantization noise is relatively high.

Contents of the invention

At present, audio watermarking based on quantization index modulation has received widespread attention and rapid development due to its superior performance in various aspects and its ability to achieve a better balance. However, the current quantization process adopts uniform quantization and fixed quantization steps. Although it is easy to implement, it is sensitive to noise and its performance in terms of robustness and imperceptibility is not good enough. Analyzing and comparing the above two watermarking algorithms, it is not difficult to find that the contradiction of audio watermarking lies in the need to improve the robustness of audio watermarking and the imperceptibility of audio watermarking. For this reason, this study proposes a new audio watermarking algorithm from these two aspects, which solves the shortcomings of existing algorithms in terms of robustness and imperceptibility, and overcomes the difficulty of high complexity. The present invention is effective Combining the robustness of the vector norm and the imperceptibility to quantization, the vector norm of the segmented wavelet approximation coefficients is converted to the transform domain through mu-law companding, and then the disturbed binary watermark image is embedded. After After the watermarking attack, the binary watermarked image is extracted. The audio watermarking algorithm proposed by the present invention not only has the characteristics of high capacity and good sound quality, but also has the advantages of good imperceptibility, good robustness, and low complexity. In the case of various watermark attacks, this method can still be used The watermark is correctly extracted, and this method can effectively resist amplitude attacks.

The present invention is characterized in that the method comprises the following steps in sequence:

Step (1) At the transmitting end, the audio watermark embedding process, the steps are as follows;

这样每帧隐藏1比特二进制水印信息，其中二进制水印图像的大小是M×M；Step (1.1) Perform two-level discrete wavelet transform DWT on the set original audio signal X={ _xi ,1≤i≤L}, the wavelet base used is Db4, where L is the number of original audio sampling points, and then Get the approximate component B={b _i ,1≤i≤L/4}, divide the approximate component into M×M non-overlapping frames S _i , 1≤i≤M×M, M is a positive integer, each frame S _i the length of

In this way, 1-bit binary watermark information is hidden per frame, where the size of the binary watermark image is M×M;

Step (1.2) according to the formula:

σ _i = ||S _i ||,

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span>$

是个1×p维向量，

is a 1×p-dimensional vector,

Calculate the vector norm σ _i of each frame S _i , 1≤i≤M×M, and let σ _max =max(σ _i ), 1≤i≤M×M;

Step (1.3) performs mu-law companding on the vector norm σ _i of each frame, and the specific calculation is as follows:

c _i =σ _i /σ _max ,

λ _i =ln(1+μc _i )/ln(1+μ),

d = λ _i mod Δ,

Δ is the preset quantization step size, 0≤Δ≤1, μ is the parameter of mu-law companding, 0≤μ≤255;

Step (1.4) Use the binary watermark image W={w _ij ,1≤i≤M,1≤j≤M} and the chaotic sequence E={e _ij ,1≤i≤M,1≤j≤M} to obtain the disturbance The watermark image W={w _ij ,1≤i≤M,1≤j≤M}:

是异或操作，W＝{w_ij,1≤i≤M,1≤j≤M}将被嵌入到原始音频信号X中，i、j分别代表图像矩阵的第i行，第j列，

is an XOR operation, W={w _ij ,1≤i≤M,1≤j≤M} will be embedded into the original audio signal X, i and j represent the i-th row and j-th column of the image matrix respectively,

If w _ij =1, modify λ _i according to the following rules:

${\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

If w _ij =0, modify λ _i according to the following rules:

λ _i '=λ _i +Δ/2-(λ _i mod Δ);

Step (1.5) utilizes the formula:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; )</span>}^{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; ,</span>$

是个1×p维向量，定义如上所述，

is a 1×p-dimensional vector, defined as above,

Calculate the modified vector norm σ _i ' and the frame S _i ', 1≤i≤M×M, and use the frame S _i ' to reconstruct the approximate component B'={bi _' ,1≤i≤L/4} ;

Step (1.6) Perform 2-stage discrete wavelet inverse transform IDWT on the approximate component B'={ _bi ',1≤i≤L/4} to obtain the watermarked audio signal X';

Step (2) At the receiving end, the audio watermark extraction process, the steps are as follows;

Step (2.1) Perform a two-level discrete wavelet transform DWT on the watermarked audio signal X'={ _xi , 1≤i≤L}, the wavelet base used is Db4, where L is defined as above, and then approximate components are obtained B'={b _i ', 1≤i≤L/4}, divide the approximate component into M×M non-overlapping frames S _i ', 1≤i≤M×M, the length of each frame S _i ' is

Step (2.2) according to the formula:

σ _i '=||S _i '||,

Calculate the vector norm σ _i ' of each frame S _i ', 1≤i≤M×M;

Step (2.3) performs mu-law companding on the vector norm σ _i ' of each frame, and the specific calculation is as follows:

c _i '=σ _i '/σ _max ,

λ _i '=ln(1+μc _i ')/ln(1+μ),

d = λ _i ' mod Δ,

Δ is the preset quantization step size, defined as above, μ is the parameter of mu-law companding, defined as above;

Step (2.4) according to:

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; and\; d</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; others</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; \&CirclePlus;</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; ,</span>$

The original watermark image W={w _ij , 1≤i≤M, 1≤j≤M} is obtained.

The blind audio watermark implementation method based on logarithmic index modulation proposed by the present invention mainly includes: using logarithmic quantification to improve the imperceptibility of the algorithm, using vector norms to improve the robustness of the algorithm, and using chaotic sequence encryption The watermark image improves the security and robustness of the watermark. The vector norm of the segmental wavelet approximation coefficients is converted to the transform domain through mu-law companding, and then embedded in the encrypted binary watermark image. After the watermark attack, the extracted Binary watermark image. The audio watermarking algorithm proposed by the present invention not only has the characteristics of high capacity and good sound quality, but also has the advantages of good imperceptibility, good robustness, and low complexity. In the case of various watermark attacks, this method can still be used The watermark is correctly extracted, and this method can effectively resist amplitude attacks.

Description of drawings

Figure 1 is the embedded module of the audio watermarking algorithm.

Figure 2 is the extraction module of the audio watermarking algorithm.

Figure 3 is a system block diagram of the audio watermarking algorithm.

Detailed ways

The blind audio watermark implementation method based on logarithmic index modulation proposed by the present invention includes two parts: a watermark embedding module and a watermark extraction module:

我们可以得到扰乱的水印图像W＝{w_ij,1≤i≤M,1≤j≤M}，若w_ij＝1，则按如下规则修改λ_i： ${\mathrm{\&lambda;}}_i^{\&prime;}=\left\{\begin{array}{c}{\mathrm{\&lambda;}}_i-\left({\mathrm{\&lambda;}}_i\mathrm{mod}\mathrm{\&Delta;}\right),\mathrm{if}(d<\mathrm{\&Delta;}/2)\\ {\mathrm{\&lambda;}}_i+\mathrm{\&Delta;}-\left({\mathrm{\&lambda;}}_i\mathrm{mod}\mathrm{\&Delta;}\right),\mathrm{if}(d>\mathrm{\&Delta;}/2)\end{array}\right.,$ 若w_ij＝0，则按如下规则修改λ_i：λ_i'＝λ_i+Δ/2-(λ_imodΔ)。利用公式： ${\mathrm{\&sigma;}}_i^{\&prime;}=({(1+\mathrm{\&mu;})}^{{\mathrm{\&lambda;}}_i^{\&prime;}}-1)*{\mathrm{\&sigma;}}_{\max }/\mathrm{\&mu;},S_i^{\&prime;}={\mathrm{\&sigma;}}_i^{\&prime;}{u}_i^T,$ 计算修改过的向量范数σ_i'和帧S_i',1≤i≤M×M，并利用帧S_i'重构近似分量B'＝{b_i',1≤i≤L/4}，对近似系数B'＝{b_i',1≤i≤L/4}进行2级的离散小波反变换IDWT，我们可以得到含水印的音频信号X'；1) Watermark embedding module: used to embed watermark information. Perform two-level discrete wavelet transform DWT on the original audio signal X={ _xi , 1≤i≤L}, where L is the number of sampling points of the original audio, and obtain the approximate component B={ _bi , 1≤i≤ L/4}, divide the approximate components into M×M non-overlapping frames S _i , 1≤i≤M×M, calculate the vector norm σ _i of each frame S _i , 1≤i≤M×M, and Let σ _max ＝max(σ _i ), 1≤i≤M×M, and calculate the vector norm σ _i of each frame as follows: c _i ＝σ _i /σ _max , λ _i ＝ln(1+μc _i )/ln(1+μ), d=λ _i modΔ, Δ is a preset quantization step size, μ is a parameter of mu-law companding. Using the binary watermark image W={w _ij ,1≤i≤M,1≤j≤M} and the chaotic sequence E={e _ij ,1≤i≤M,1≤j≤M} and the formula

We can get the disturbed watermark image W={w _ij ,1≤i≤M,1≤j≤M}, if w _ij =1, modify λ _i according to the following rules: ${\mathrm{\&lambda;}}_i^{\&prime;}=\left\{\begin{array}{c}{\mathrm{\&lambda;}}_i-\left({\mathrm{\&lambda;}}_i\mathrm{mod}\mathrm{\&Delta;}\right),\mathrm{if}(d<\mathrm{\&Delta;}/2)\\ {\mathrm{\&lambda;}}_i+\mathrm{\&Delta;}-\left({\mathrm{\&lambda;}}_i\mathrm{mod}\mathrm{\&Delta;}\right),\mathrm{if}(d>\mathrm{\&Delta;}/2)\end{array}\right.,$ If w _ij =0, modify λ _i according to the following rule: λ _i '=λ _i +Δ/2-(λ _i mod Δ). Use the formula: ${\mathrm{\&sigma;}}_i^{\&prime;}=({(1+\mathrm{\&mu;})}^{{\mathrm{\&lambda;}}_i^{\&prime;}}-1)*{\mathrm{\&sigma;}}_{\max }/\mathrm{\&mu;},S_i^{\&prime;}={\mathrm{\&sigma;}}_i^{\&prime;}{u}_i^T,$ Calculate the modified vector norm σ _i ' and the frame S _i ', 1≤i≤M×M, and use the frame S _i ' to reconstruct the approximate component B'={b _i ',1≤i≤L/4} , we can obtain the watermarked audio signal X' by performing a two-level inverse discrete wavelet transform IDWT on the approximation coefficient B'={ _bi ',1≤i≤L/4};

2) Watermark extraction module: used to extract watermark information. Carry out two-level discrete wavelet transform DWT on the audio watermark signal X'={ _xi ,1≤i≤L}, and obtain the approximate component B'={ _bi ',1≤i≤L/4}, divide the approximate component into M×M non-overlapping frames S _i ', 1≤i≤M×M, according to the formula: σ _i '=||S _i '||, calculate the vector norm σ _i ' of each frame S _i ', 1≤i≤M×M, the vector norm σ _i ' of each frame is calculated as follows: c _i '=σ _i '/σ _max , λ _i '=ln(1+μc _i ')/ln(1+ μ), d=λ _i 'modΔ, Δ is the preset quantization step size, μ is the parameter of mu-law companding, according to $w_{\mathrm{ij}}=\left\{\begin{array}{c}0,\mathrm{if}(d>\mathrm{\&Delta;}/4\mathrm{and\; d}<3*\mathrm{\&Delta;}/4)\\ 1,\mathrm{if}\left(\mathrm{others}\right)\end{array}\right.$ and $W=W\&CirclePlus;\mathrm{E.},$ We can get the original watermark image W={w _ij , 1≤i≤M, 1≤j≤M}.

Below in conjunction with accompanying drawing, describe content of the present invention in detail:

Figure 1 is an audio watermark embedding module based on logarithmic index modulation. As shown in Figure 1, the original audio signal X is subjected to two-level discrete wavelet transform DWT, and the obtained approximate components are divided into M×M non-overlapping frames, and the vector norm of each frame is calculated, and then mu-law compression Expand, embed the binary watermark image W encrypted by the chaotic sequence, and then perform mu-law companding, calculate the modified vector norm and this frame, repeat the above process until all the watermark bits are embedded, and use the modified The approximate component is reconstructed from the frame of , and the inverse discrete wavelet transform IDWT is performed on the approximate component, we can get the audio signal X' with watermark.

Figure 2 is an audio watermark extraction module based on logarithmic quantization index modulation. As shown in Figure 2, a two-level discrete wavelet transform DWT is performed on the watermarked audio signal X', and the obtained approximate components are divided into M×M non-overlapping frames, and the vector norm of each frame is calculated, and then mu -law companding, extracting binary watermark bits, decrypting with chaotic sequence, and obtaining the original binary watermark image W.

Figure 3 is a system block diagram of the audio watermarking algorithm. As shown in Figure 3, the watermark information is embedded into the original carrier through the watermark embedding module, and after various attacks, the watermark information is extracted through the watermark extraction module.

Claims (1)

1. A blind audio watermark implementation method based on logarithm quantization index modulation, the present invention is characterized in that, described method contains following steps successively: Step (1) At the transmitting end, the audio watermark embedding process, the steps are as follows; Step (1.1) Perform two-level discrete wavelet transform DWT on the set original audio signal X={ _xi ,1≤i≤L}, the wavelet base used is Db4, where L is the number of original audio sampling points, and then Get the approximate component B={b _i ,1≤i≤L/4}, divide the approximate component into M×M non-overlapping frames S _i , 1≤i≤M×M, M is a positive integer, each frame S _i the length of

In this way, 1-bit binary watermark information is hidden per frame, where the size of the binary watermark image is M×M; Step (1.2) according to the formula: σ _i =||S _i ||, ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span>$

is a 1×p-dimensional vector, Calculate the vector norm σ _i of each frame S _i , 1≤i≤M×M, and let σ _max =max(σ _i ), 1≤i≤M×M; Step (1.3) performs mu-law companding on the vector norm σ _i of each frame, and the specific calculation is as follows: c _i =σ _i /σ _max , λ _i =ln(1+μc _i )/ln(1+μ), d = λ _i mod Δ, Δ is the preset quantization step size, 0≤Δ≤1, μ is the parameter of mu-law companding, 0≤μ≤255; Step (1.4) uses the binary watermark image W={w _ij ,1≤i≤M,1≤j≤M} and the chaotic sequence E={e _ij ,1≤i≤M,1≤j≤M} to obtain the disturbance The watermark image W={w _ij ,1≤i≤M,1≤j≤M}:

is an XOR operation, W={w _ij ,1≤i≤M,1≤j≤M} will be embedded into the original audio signal X, i and j represent the i-th row and j-th column of the image matrix respectively, If w _ij =1, modify λ _i according to the following rules: ${\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$ If w _ij =0, modify λ _i according to the following rules: λ _i '=λ _i +Δ/2-(λ _i mod Δ); Step (1.5) utilizes the formula: ${\mathrm{\&sigma;}}_i^{\&prime;}=({(1+\mathrm{\&mu;})}^{{\mathrm{\&lambda;}}_i^{\&prime;}}-1)*{\mathrm{\&sigma;}}_{\max }/\mathrm{\&mu;},$ is a 1×p-dimensional vector, defined as above, Calculate the modified vector norm σ _i ' and the frame S _i ', 1≤i≤M×M, and use the frame S _i ' to reconstruct the approximate component B'={bi _' ,1≤i≤L/4} ; Step (1.6) Perform 2-stage discrete wavelet inverse transform IDWT on the approximate component B'={ _bi ',1≤i≤L/4} to obtain the watermarked audio signal X'; Step (2) At the receiving end, the audio watermark extraction process, the steps are as follows; Step (2.1) Perform a two-level discrete wavelet transform DWT on the watermarked audio signal X'={ _xi , 1≤i≤L}, the wavelet base used is Db4, where L is defined as above, and then approximate components are obtained B'={b _i ', 1≤i≤L/4}, divide the approximate component into M×M non-overlapping frames S _i ', 1≤i≤M×M, the length of each frame S _i ' is

Step (2.2) According to the formula: σ _i '=||S _i '||, Calculate the vector norm σ _i ' of each frame S _i ', 1≤i≤M×M; Step (2.3) performs mu-law companding on the vector norm σ _i ' of each frame, and the specific calculation is as follows: c _i '=σ _i '/σ _max , λ _i '=ln(1+μc _i ')/ln(1+μ), d = λ _i ' mod Δ, Δ is the preset quantization step size, defined as above, μ is the parameter of mu-law companding, defined as above; Step (2.4) according to: ${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; and\; d</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; others</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$ $\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; \&CirclePlus;</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; ,</span>$ The original watermark image W={w _ij , 1≤i≤M, 1≤j≤M} is obtained.

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