CN101038771A - Novel method of digital watermarking for protecting literary property of music works - Google Patents
- ️Wed Sep 19 2007
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- CN101038771A CN101038771A CNA2006100675801A CN200610067580A CN101038771A CN 101038771 A CN101038771 A CN 101038771A CN A2006100675801 A CNA2006100675801 A CN A2006100675801A CN 200610067580 A CN200610067580 A CN 200610067580A CN 101038771 A CN101038771 A CN 101038771A Authority
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- China Prior art keywords
- watermark
- embedding
- synchronization code
- information
- audio data Prior art date
- 2006-03-18 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Abstract
本发明属于信息安全,多媒体信息处理领域,具体为一种用于音乐作品版权保护的数字水印新方法,主要包括同步码、水印嵌入,及检测。本发明首先将音乐作品进行分段处理,然后再将每个音乐数据段划分成前后两个部分以进行信息嵌入。在前部分通过修改多个采样值的统计均值嵌入同步码,而后部分用于水印信息的嵌入,其嵌入过程为,首先对音乐数据段进行DWT,再对小波域的低频系数进行DCT,然后利用自适应量化策略将加密后的水印信息嵌入到DCT域的低中频系数中,最后通过逆变换过程及音乐数据段重新组合得到嵌入水印信息的数字音乐作品。数字水印检测是嵌入过程的逆过程。本发明不依赖于对阈值的调整,可应用于不同种类的音乐作品中。
The invention belongs to the fields of information security and multimedia information processing, and specifically relates to a new digital watermark method for copyright protection of music works, which mainly includes synchronization code, watermark embedding, and detection. The invention first divides the music works into segments, and then divides each music data segment into two parts before and after to carry out information embedding. In the first part, the synchronization code is embedded by modifying the statistical mean value of multiple sampling values, and the latter part is used to embed the watermark information. The embedding process is as follows: first, perform DWT on the music data segment, and then perform DCT on the low-frequency coefficients in the wavelet domain, and then use The adaptive quantization strategy embeds the encrypted watermark information into the low intermediate frequency coefficients in the DCT domain, and finally obtains the digital music works with embedded watermark information through the process of inverse transformation and recombination of music data segments. Digital watermark detection is the reverse process of embedding process. The present invention does not depend on the adjustment of the threshold, and can be applied to different kinds of music works.
Description
Technical field
The invention belongs to Information hiding and digital watermark technology field in the multi-media information security; be specifically related to a kind of digital audio frequency watermark new method; can effectively resist time domain synchronization attack very difficult in the audio frequency watermark technology, have great practical value for the copyright protection of musical works.
Background technology
Along with the develop rapidly of network technology (particularly Internet technology) with the multimedia messages treatment technology, the intellectual property protection of copyright becomes the key issue that presses for solution.Under this background, digital watermark technology has been subjected to people's common concern, and has become a focus of network information security research field.According to range of application, can be divided into image watermark, video watermark and audio frequency watermark etc. to digital watermarking usually.In recent years, a lot of for the research of image watermark and video watermark (especially image watermark), and the research of relevant digital audio frequency watermark seems and relatively lags behind.Especially, it is deficient unusually especially effectively to resist the strong steady audio-frequency water mark method of synchronization attack.
So-called synchronization attack (Synchronization attack) is not that the attack of this kind of finger can be removed watermark information from contain the watermark object, and is meant that it can be deformed to digital watermarking detecting device and detect not come out (promptly changing the watermark embedded location).By the end of at present, people mainly adopt the steady audio-frequency water mark scheme of four kinds of measures design synchronous attack resistants, are respectively exhaustive search, the spread-spectrum watermark spreading code combines, utilizes original audio key character, synchronous code etc.Wherein, exhaustive search scheme has that calculated amount is big, the more high weakness of false alarm rate; The spread-spectrum watermark spreading code scheme of combining can't realize the blind Detecting of watermark information; Utilize original audio key character scheme to have feature point extraction instability, required threshold value and too much be unfavorable for deficiencies such as practical application.By contrast, the synchronous code scheme has more tangible technical advantage.But there is following deficiency in the present watermark embedding method majority based on the synchronous code scheme: the Barker code length that (1) is adopted is too short, causes that easily vacation synchronously, has influenced the robustness of synchronizing signal; (2) only synchronous code is embedded on the single sampled value of DAB, greatly reduces the ability (particularly attack such as resampling, MP3 compression) that opposing is attacked; (3) fail to determine quantization step (promptly having adopted fixing watermark embedding depth), influenced the not sentience of digital watermarking in conjunction with the auditory masking characteristic.
Pertinent literature is as follows:
[1]Huang J W,Wang Yong,Shi Y.Q.A Blind Audio Watermarking Algorithm WithSelf-synchronization.In:Proceedings of IEEE International Symposium on Circuits and System,Arizona,USA,2002,3:627-630.
Summary of the invention
In view of above-mentioned existing in prior technology problem; the present invention has designed a kind of novel method of digital watermarking that is used for protecting literary property of music works; this method is chosen 16 more sane Barker codes as sync mark; and, adopt the adaptive quantizing strategy that watermark information is embedded in the DAB in hybrid domain in conjunction with the auditory masking characteristic simultaneously by revising the average statistical embedding synchronous code of a plurality of sampled values.
Basic functional principle of the present invention is: at first original audio signal is carried out staging treating, and then each audio data section is divided into former and later two parts to carry out the information embedding.Wherein, previous section is used for the spatial domain and embeds synchronizing signal, considers the instability of single sampled value, so in the telescopiny of synchronizing signal, adopted the method for the average statistical of revising a plurality of sampled values, has improved the robustness of synchronous code.Aft section is used for the hybrid domain embed watermark information.And the concrete telescopiny of watermark information is, at first audio data section (aft section) is carried out DWT, and the low frequency coefficient to wavelet field carries out DCT again, utilizes the watermark information after the adaptive quantizing strategy will be encrypted to be embedded in the Low Medium Frequency coefficient in DCT territory at last.Carry out just because of the embedding of watermark is a energy according to audio frequency,, can be applicable in different types of musical works so the present invention does not rely on the adjustment to threshold value.
Audio frequency watermark significant synchronously.When carrying out real-time watermark detection, detecting device must be by detecting the reference position that synchronizing information determine that watermark embeds accurately.And the effect of synchronous code in the isochronous audio watermark is most important, and can synchronous code accurately locate to have determined whether detecting device is effective, so the robustness of synchronous code also just becomes the key of watermark detection system.
The novel method of digital watermarking that is used for protecting literary property of music works of the present invention; this method can be by choosing 16 more sane Barker codes as sync mark, determine quantization step, synchronous code is embedded into the measures such as average statistical of a plurality of sampled values in conjunction with the digital audio content self-adaptation, with digital watermark signal in hybrid domain is embedded in original digital audio.Simultaneously, emulation experiment shows that also audio-frequency water mark method proposed by the invention not only has preferably not sentience, and all has robustness preferably for Audio Processing such as superimposed noise, resampling, re-quantization, shearing, MP3 compression and attack.In addition; the present invention has an outstanding advantage; promptly highly depend on adjustment the method that in former document, proposes to some thresholding or supposition parameter; can not add in the different types of musical works of being applied to of modification; and need not characteristics such as initial carrier audio frequency when extracting watermark, this has strengthened it greatly and has been used for the practicality of DAB Works copyright protection.
Description of drawings
The present invention has four accompanying drawings, wherein,
Fig. 1: the structure that is used for the embedded data of novel method of digital watermarking of protecting literary property of music works
Fig. 2: the embedding flow process that is used for the novel method of digital watermarking of protecting literary property of music works
Fig. 3: the testing process that is used for the novel method of digital watermarking of protecting literary property of music works comprises that synchronous code detects and two key links of watermark signal extraction
Fig. 4 (a): original audio signal
Fig. 4 (b): original watermark image
Fig. 4 (c): the digital audio and video signals behind the embed watermark
Fig. 4 (d): the watermarking images that from contain the watermark sound signal, extracts
Embodiment
The specific implementation of the novel method of digital watermarking that is used for protecting literary property of music works of the present invention is shown in accompanying
drawing2, accompanying
drawing3; embedding and the detection method that is used for the novel method of digital watermarking of protecting literary property of music works of the present invention comprises following concrete steps:
Digital watermarking of the present invention embeds strategy: be embedded in synchronizing signal in spatial domain, (DCT and DWT) is embedded in watermark information in hybrid domain.Suppose that the original digital audio signal is A={a (i), 0≤i<Length}.Wherein, Length is the number of voice data, a (i) ∈ 0,1,2 ..., (2 p-1) } be the range value of i voice data, p is the employed bit number of each data of expression.Suppose binary bitmap be W={w (i, j), 0≤i<M, 0≤j<N}.Wherein, (i, j) { 0,1} represents capable, the j row pixel value of the i of binary bitmap to ∈ to w.The assumes synchronization sign indicating number is F={f (i), 0≤i<Lsyn}, wherein, f (i) ∈ 0, and 1} (for the ease of using, former Barker code is carried out simple transformation here, promptly+1 → 0 ,-1 → 1), Lsyn is the length of synchronous code.Then the blind watermark embed process of ADAPTIVE MIXED domain digital audio (committed step) can be described below.
1 pre-service
In order to eliminate the pixel space correlativity of binary bitmap, improve the security performance of whole digital watermarking system, guarantee still can recover watermark whole or in part after a DAB part is damaged, should at first carry out scrambling encryption to binary bitmap.For this reason, the present invention at first introduces the Arnold conversion, is the secure watermark matrix W with binary bitmap W scrambling encryption 1, W wherein 1={ w 1(i, j), 0≤i<M, 0≤j<N}.
In order further to improve attacking ability synchronously such as opposing shearing, translation, so that the DAB partial data still can guarantee the effectively reliable of watermark detection after losing, the present invention at first carries out staging treating to the original digital audio signal, and then each audio data section is divided into length is L 1And L 2Two parts and embed synchronous code and watermark information respectively.Wherein, i audio data section can be expressed as
Here, L=L 1+ L 2, L 1=Lsyn * n, L 2=M * N * 2 H+1, H is a wavelet transformation progression, n is constant (the present invention is chosen for 5).
If certain audio data section is A 0(its length is L 1And L 2Two parts be A 1 0And A 2 0), then the telescopiny of synchronous code and digital watermark information is as follows.
2 synchronous codes embed
In order to guarantee the well balanced of not sentience and robustness, the present invention adopts the method for revising a plurality of sampled values (n sampled value), synchronizing information is embedded in the average statistical of sampled value, and concrete steps are:
(1) with A 1 0Syn is divided into the Lsyn section by the synchronous code length L, each section PA 1 0(m) contain n sampled point, promptly
PA 1 0 ( m ) = { p a 1 0 ( m ) ( i ) = a 1 0 ( i + m × n ) , 0 ≤ i < n , 0 ≤ m < Lsyn }
(2) calculate PA 1 0(m) mean value, promptly
PA 1 0 ( m ) ‾ = 1 n Σ i = 0 n - 1 pa 1 0 ( m ) ( i ) , ( 0 ≤ m < Lsyn )
(3) adopt quantization method to embed synchronous code, promptly to each section PA 1 0(m), revise its average
To embed a bit synchronization sign indicating number.The modification strategy is:
pa 1 0 ′ ( m ) ( i ) = pa 1 0 ( m ) ( i ) + ( PA 1 0 ′ ( m ) ‾ - PA 1 0 ( m ) ‾ )
Wherein,
PA 1 0 ( m ) = { pa 1 0 ( m ) ( i ) , 0 ≤ i < n }For revising preceding sampled value,
PA 1 0 ′ = { pa 1 0 ′ ( m ) ( i ) , 0 ≤ i < n }Be amended sampled value, and have
Wherein, mod is a modulo operation, S 1Be quantization step.
The embedding of 3 watermark signals
(1) DWT of audio data section (aft section).To each audio data section A 2 0Carry out H level wavelet transformation, and obtain wavelet coefficient A 2 0H, D 2 0H, D 2 0H-1..., D 2 01Wherein, A 2 0HBe audio data section A 2 0The H level of wavelet transformation is similar to component, D 2 01..., D 2 0H-1, D 2 0HBe respectively audio data section A 2 0The details component of the 1st~H level of wavelet transformation.
(2) DCT of approximate component.Consider that the approximate component of wavelet transformed domain can effectively resist various interference, select the approximate component A of H level wavelet transformation here 2 0HCarry out DCT and embed watermark.
A 2 0 HC = DCT ( A 2 0 H ) = { a 2 0 ( t ) HC , 0 ≤ t < L 2 / 2 H }
(3) embedding of watermark signal.Be the robustness that guarantees audio frequency watermark and sentience not, the present invention is according to human auditory system's frequency domain masking characteristics, adopts quantization strategy that watermark information is embedded into the Low Medium Frequency part in DCT territory, promptly quantizes M * N DCT coefficient before the modulation, obtains A 2 0 ' HC, wherein:
A 2 0 ′ HC = a 2 0 ′ ( t ) HC , 0 ≤ t < M × N a 2 0 ( t ) HC , M × N ≤ t < L 2 / 2 H
Quantizing rule is as follows:
Wherein, 0≤i<M, 0≤j<N, S 2Be quantization step.
(4) inverse DCT.To the audio data section A behind the embed watermark 2 0 ' HCDo inverse DCT.
A 2 0 ′ H = IDCT ( A 2 0 ′ HC )
(5) contrary DWT.With A 2 0 ' HReplace A 2 0HAnd carry out the contrary DWT of H level, obtain containing the voice data segment signal A of watermark 2 0 '
4 circulations embed
Be to resist shearing, translation etc. to attack synchronously, increase the robustness of watermark, repeating
step2~3 carries out the embedding (promptly synchronous code and watermark information being adopted the strategy that circulates and embed) of synchronous code and watermark information to other audio data section.
The self-adaptation of quantization step is chosen
Concerning embed scheme based on the audio frequency watermark that quantizes, choosing of quantization step is most important.Because quantization step and watermark embed strength are closely related, the quantization step value is big more, digital watermarking robust performance good more (but simultaneously also easier of audio frequency introducing distortion).Choose and determine that quantization step should take into full account DAB own characteristic and visual masking characteristic.Yet the existing audio frequency watermark scheme that embeds has generally adopted the uniform quantization strategy, promptly whole DAB is adopted an identical quantization step.Like this, if the quantization step value is less, then can influence the anti-aggressiveness of digital watermarking; And if the quantization step value is bigger, then can bring considerable influence to digital audio quality.In addition, different carrier audio frequency is only adopted different quantization step values and could be reached reasonable concealment effect separately.
In order effectively to overcome the existing deficiency of uniform quantization strategy, take into account the practical application (all determine a quantization step if embed point to each, calculated amount is too big) of method simultaneously, the present invention will determine quantization step S in conjunction with whole digital audio content in time domain 1, in frequency domain, determine quantization step S in conjunction with the audio data section content 2, promptly
At first, determine quantization step S according to the time domain masking characteristic 1(being used for synchronous code embeds) has
Wherein, s a=| A| represents the absolute value average (being the average of peak value) of original digital audio A.
Then, determine quantization step S2 (being used for watermark information embeds) in conjunction with frequency domain masking characteristics self-adaptation, concrete steps are
(1) audio data section A 2 0(A 2 0Implication the same) DWT.To audio data section A 2 0Carry out H level wavelet transformation, and obtain wavelet coefficient A 2 0H, D 2 0H, D 2 0H-1..., D 2 01Wherein, A 2 0HBe audio data section A 2 0The H level of wavelet transformation is similar to component, and D 2 0H, D 2 0H-1..., D 2 01Be respectively audio data section A 2 0The details component of the 1st~H level of wavelet transformation.
(2) DCT of approximate component.Here select the approximate component A of H level wavelet transformation 2 0HCarry out DCT.
A 2 0 HC = DCT ( A 2 0 H ) = { a 2 0 ( t ) HC , 0 ≤ t < L 2 / 2 H }
(3) quantization step S 2Self-adaptation choose.Because watermark information has been embedded in preceding M * N the coefficient in DCT territory, so disturb in order to reduce digital watermarking, to guarantee that watermark extraction process can effectively calculate quantization step, the present invention is in conjunction with the audio data section content and utilize back M * N the coefficient self-adaptation in DCT territory to determine quantization step S 2Promptly
(
Be downward bracket function),
S b = | A ^ 2 0 HC ‾ | = Σ t = M × N L 2 / 2 H - 1 | a 2 0 ( t ) HC | M × NThe leaching process of digital watermarking
The ADAPTIVE MIXED domain digital audio water mark method of discussion of the present invention belongs to blind watermark method, does not need the original audio carrier when promptly detecting digital watermark signal.Whole digital watermarking testing process comprises that synchronous code detects and two key links of watermark signal extraction, as shown in Figure 3.
The detection of 1 synchronous code
Here said synchronous code detects, and is meant that (size is L to detection window 1) whether contain embedded synchronous code information in the audio data section that covered.Its job step is:
(1) job step of choosing according to the self-adaptation of quantization step, self-adaptation is determined quantization step S 1 *
(2) job step that embeds according to synchronous code is calculated audio data section (being window institute cover part) preceding n * m sampled value PA respectively *(m) mean value
PA *(m)={pa *(m)(i)=a *(i+m×n),0≤i<n,0≤m<Lsyn}
(3) extract synchronous code information F '.Fetch strategy is
(4) in order effectively to avoid false synchronia to take place, the frame synchronization code that the present invention has adopted communications field comparative approach is by turn determined synchronous code, if promptly synchronous code F ' that is extracted and former synchronous code F are identical, then think to have detected embedded synchronous code information.
The extraction of 2 watermark signals
Here said watermark signal extracts, and is meant that audio data section behind the Secondary Synchronization Code (makes that this audio data section is A 2 0*, its length is L 2) the interior watermark information that extracts.Its job step is:
(1) job step of choosing according to the self-adaptation of quantization step is in conjunction with audio data section A 2 0*Content-adaptive is determined quantization step S 2 *
(2) to audio data section A 2 0*Carry out H level DWT, obtain wavelet coefficient A 2 0*H, D 2 0*H, D 2 0*H-1..., D 2 0*1
(3) pairing approximation component A 2 0*HDo dct transform
A 2 0 * HC = DCT ( A 2 0 * H ) = { a 2 0 * ( t ) HC , 0 ≤ t < L 2 / 2 H }
(4) extract watermark information, the extraction formula is
(5) the watermark information W ' that is extracted is carried out inverted and disorderly encrypt, just can obtain binary bitmap
W *={w *(i,j),0≤i<M,0≤j<N}。
Need to prove, because the present invention has adopted circulation to embed strategy to synchronous code and watermark information, so the digital watermarking testing process will extract a plurality of binary bitmap W r *(r=1,2 ..., R).For this reason, need further to calculate final digital watermarking according to " majority principle "
Promptly
Here,
W r * ( i , j ) ∈ W r * , w ^ * ( i , j ) ∈ W ^ * .In addition, influence for subjective and objective factors such as the experience of eliminating the observer, physical qualification, experiment conditions, (Normalized Cross-Correlation NC), carries out quantitative evaluation to the watermark that extracts and the similarity of original watermark must to adopt normalized correlation coefficient.
Below our good effect of bringing in conjunction with experimental data explanation the present invention.
Provided the experimental result that detects performance test, anti-attack ability test respectively, and contrasted with document [1] method.In the experiment, selected initial carrier is that sample frequency is 44.1kHz, and resolution is 16 bits, and length is 9.75 seconds monophony digital audio and video signals.64 * 64 bianry image has been adopted in digital watermarking.Wavelet transformation has adopted common Daubechies-1 wavelet basis.Wavelet transformation progression is chosen for H=2, and to have selected code length for use be that 16 Barker code 1111100110101110 is as synchronizing signal.Because the watermark of adopting is visual sensuously, so the watermark information that extracts is easy to distinguish.
The anti-attack ability test
In order to detect robustness of the present invention, emulation experiment has been carried out a series of attacks to the watermark sound signal that contains of the present invention and document [1] method respectively, comprising: resampling, and re-quantization, Gaussian noise is disturbed, MP3 compression and shearing etc.Wherein
(1) resampling.The sampled audio signal frequency is dropped to 22.05kHz, 11.025kHz, 8kHz, restore and be former sample frequency 44.1kHz.
(2) re-quantization.Be 8 bits with sound signal from 16 bit quantizations earlier, be quantified as 16 bits again.
(3) superimposed noise.To digital audio and video signals add in time domain that average is 0, mean square deviation is 0.01 white Gaussian noise.
(4) MP3 compression.Earlier sound signal is carried out MP3 compression (being respectively 320k, 256k, 112k, 64k, 48k, 32k by frequency), decompress again.
(5) shear.Shear audio frequency front 10% part and random shearing audio frequency middle 10% respectively.
Table 1 has provided the anti-attack ability results of comparison (the Y-PSNR PSNR that comprises the normalized correlation coefficient NC of the watermarking images that extracted, digital watermarking and distortion rate BER, DAB) of the present invention and document [1] method.
Emulation experiment also shows, audio-frequency water mark method proposed by the invention not only has preferably not sentience (referring to the PSNR in the table 1), and all has robustness (referring to NC in the table 1 and BER, particularly attack such as resampling, MP3 compression) preferably with attacking for Audio Processing such as superimposed noise, resampling, re-quantization, shearing, MP3 compressions.In addition, the hybrid domain audio frequency watermark embedding grammar that the present invention proposes also has characteristics such as calculating simply, realize easily, need not when extracting watermark the initial carrier audio frequency, and this has strengthened it greatly and has been used for the practicality of DAB Works copyright protection.
Table 1 digital watermarking is to the resistivity (audio frequency 1) of part conventional attack
Do not attack | Weightization | Resampling 22.05kHz | Resampling 11.025kHz | Resampling 8kHz | Gaussian noise | Shear front 10% | ||
Document [1] | NC | 1.0000 | 1.0000 | 0.4087 | 0.3618 | 0.3550 | 0.9619 | 1.0000 |
BER | 0 | 0 | 0.5059 | 0.4773 | 0.4910 | 0.0210 | 0 | |
PSNR | 48.3965 | 44.5576 | 43.4559 | 27.3970 | 27.2939 | 41.6215 | 49.4736 | |
The present invention | NC | 1.0000 | 1.0000 | 0.9935 | 0.6624 | 0.5595 | 0.9652 | 1.0000 |
BER | 0 | 0 | 0.0037 | 0.2241 | 0.3135 | 0.0200 | 0 | |
PSNR | 48.3818 | 44.5366 | 43.4371 | 27.3978 | 27.2955 | 41.5931 | 49.3505 | |
Shear middle 10% | Mp3-320k | Mp3-256k | Mp3-112k | Mp3-64k | Mp3-48k | Mp3-32k | ||
Document [1] | NC | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.3925 | 0.3838 | 0.3722 |
BER | 0 | 0 | 0 | 0 | 0.5183 | 0.5291 | 0.4949 | |
PSNR | 48.2568 | 48.4017 | 48.4021 | 48.3810 | 47.5854 | 39.3883 | 42.3683 | |
The present invention | NC | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9948 | 0.9489 | 0.8096 |
BER | 0 | 0 | 0 | 0 | 0.0029 | 0.0295 | 0.1179 | |
PSNR | 48.3577 | 48.3881 | 48.3894 | 48.3573 | 47.5052 | 39.3810 | 42.3273 |
Digital watermarking is to the resistivity (audio frequency 2) of part conventional attack
Do not attack | Weightization | Resampling 22.05kHz | Resampling 11.025kHz | Resampling 8kHz | Gaussian noise | Shear front 10% | ||
Document [1] | NC | 1.0000 | 0.9996 | 0.3733 | 0.3773 | 0.3702 | 0.9161 | 1.0000 |
BER | 0 | 0.0002 | 0.4983 | 0.4939 | 0.4954 | 0.0435 | 0 | |
PSNR | 37.5415 | 37.3409 | 37.5850 | 22.8633 | 20.8454 | 27.9397 | 40.9718 | |
The present invention | NC | 1.0000 | 0.9996 | 1.0000 | 0.8932 | 0.7778 | 0.9212 | 1.0000 |
BER | 0 | 0.0002 | 0 | 0.0645 | 0.1414 | 0.0443 | 0 | |
PSNR | 37.3874 | 37.1785 | 37.3815 | 22.8496 | 20.8420 | 28.0767 | 40.6236 | |
Shear middle 10% | Mp3-320k | Mp3-256k | Mp3-112k | Mp3-64k | Mp3-48k | Mp3-32k | ||
Document [1] | NC | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.3619 | 0.3638 | 0.3667 |
BER | 0 | 0 | 0 | 0 | 0.5010 | 0.4932 | 0.5215 | |
PSNR | 36.8543 | 37.3108 | 37.3107 | 36.8539 | 36.3864 | 35.3564 | 35.8408 | |
The present invention | NC | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9528 | 0.9748 | 0.9104 |
BER | 0 | 0 | 0 | 0 | 0.0273 | 0.0144 | 0.0527 | |
PSNR | 36.7003 | 37.1747 | 37.1777 | 36.7516 | 36.2663 | 35.3669 | 35.8112 |
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