5.1 Robustness Tests
The robustness properties are very important for every watermarking technique, because the watermark is supposed to survive under any trial of destructing the audio signal, which does not degrade the audio quality.
We made the robustness tests with the casual audio processing procedures. The most often used audio processing procedures are the conversion between digital and analog formats and the data compression. To examine the robustness, the recovery accuracy rates of the D to A
to D conversions and the MP3 and WMA format compressions were checked.
5.1 Additive Noise
Some noise would be introduced into the audio as the signal is transmitted, and the audio quality may be degraded because of the additive noise. The additive noise on the watermarked audio not only may lower the quality of audio signal, it may also destroy the hidden information. In this D to A to D experiment, the noise was introduced by the D/A and the A/D conversion from the interpolation and quantization stage during the process, and by the audio transmission line while the line is not lossless resistant. The output of watermarked audio added noise will be examined for the recovery accuracy rate and was compared with the accuracy rate of noiseless audio.
5.2 Compression
The lossy audio compression would remove some perceptually insignificant information from the audio signal. The watermark extraction accuracy would be influenced because some part of the watermarked information may be destroyed during the lossy audio compression. At first glance, we thought the accuracy rate reduction would vary with the different compression bit rate. Tests with varied bit rate of MP3 compression and WMA compression were made, as Fig. 32 illustrated.
Though there exists some performance degradation after lossy audio compression, there is no obvious difference between the varied bit rates.
1
10
100
1000
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
delay distance (msec)
watermark-embedding rate
Fig. 31 Tradeoff between the delay distance and watermark-embedding rate A=0.7; Wps=2~256, step 2 time; d0=0.8, 1msec, d1=1.1~1.9msec, step 0.1msec
We turn to test the recovery accuracy under varying
echo magnitude and varying watermark-embedding rates, where the compression bit rate was assigned as the typical value 128k bps on both MP3 and WMA formats.
5.3 Threshold Check
A modified echo data hiding system with an energy threshold check module in the watermark embedding stage was set up following the description in Chapter 3.
To strengthen the usage of energy threshold check, a special audio piece, which has many silent or small energy segments, was generated especially for this experiment. Near 30% of the samples in this generated
audio signal have small energy, which is under two
quantization steps, and half of the small energy samples (15% of all samples) are totally silent.
The threshold of small energy is defined as five, which represents the average amplitude of the samples is lower than or equal to two quantization steps, while the audio signal is in 16-bit PCM format. About 15% of the blocks should be skipped after the silent energy check;
and about 30% of the blocks should be skipped after the small energy check. Theoretically, when 15% of the samples are silent, the watermark extraction error caused by the misread in silent blocks would be about 7.5%, when the random error rate is assumed as 50%; and the error caused by the small energy blocks would be approximately 15% under the same reason.
MP3 Compression
0.7 0.8 0.9 1 1.1
embedded 320 256 224 192 160 128 112 96 80 64 56 48 40 32
MP3 bit rate
degrading rate
Wps=2 Wps=8
WMA Compression
0.7 0.8 0.9 1 1.1
embedded 160 128 96 80 64 48
WMA bit rate
degrading rate
Wps=2 Wps=8
Fig. 32 Reduction of the recovery accuracy rate caused by MP3 and WMA compression (varying compression bit rate)
A=0.7; Wps=2,8; d0=0.8msec, d1=1.3msec; audio sampling rate=44.1kHz; MP3 bit rate=32~320k, WMA bit rate=48~160k, as shown above.
The result of watermark extraction after the energy
threshold check will be compared with the result without energy threshold check. The increase of the recovery accuracy rate after adding energy threshold check module with varying magnitude is shown in Fig. 33. The examination of varying magnitude was done by assigning fixed watermark embedding rate as 2 and 16, and delay distance as 0.6msec, where d0=0.7, 0.8 and 0.9msec were given. The results of this experiment are a little different from the theoretical prediction, because the increase of recovery accuracy rate is a little smaller than the predicted value. The variation is based on the energy for threshold check that is calculated as an average value of the block, while in each block, the samples may include both some
silent or small energy ones and some large energy ones.
The magnitude of echoes influences the recovery accuracy rate very much as discussed in prior chapters. In the experiment, we have a peak of accuracy increase at magnitude 0.4 for skipping the silent blocks and a peak at magnitude 0.3 for skipping the small energy blocks, while the minimum increase of both conditions occur at magnitude 0.5. When the amplitude is one, the echo added amplitude would round up to two only when the magnitude of echo is larger than 0.5, and would round down to one when the magnitude is smaller than 0.5. As a result, much more of the quantization errors occur at echo magnitude 0.4.
Threshold with varying A
0 5 10 15 20
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
magnitude
accuracy increase(%)
silence, Wps=2 under 2, Wps=2 silence, Wps=16 under 2, Wps=16
Fig. 33 Increase of accuracy rate after energy threshold check (varying magnitude)
A=0.2~0.9, step 0.1; Wps=2, 16; d0=0.7, 0.8, 0.9msec, delay distance=0.6msec; energy threshold=1, 5.
The same situation of round off error happens when the average amplitude is two. The value of amplitude is easier to round down at magnitude 0.3 and easier to round up at 0.5 than at any other position. The round off property of the decimal system is the cause of the peak and valley of the accuracy increase curves after the energy threshold check. When the amplitude with rounded down segments are skipped and no watermark is embedded, errors caused by the round off error can be avoided and the recovery accuracy rate is increased.
When the test of adding energy check module is made with varying watermark-embedding rate, there also exists some increase of the recovery accuracy rate, as Fig.
34 illustrates. Although no obvious peak or valley occur in the curves, more accuracy increase is shown at the higher watermark-embedding rate. The influence of this parameter has been discussed in prior chapters; the smaller the block size is, the easier the extraction error that may occur, because the small block makes it hard to average the energy change in the segment and to avoid error.
Bypassing the silent and small energy segments by adding the energy threshold check does help to reduce the errors caused by these segments. The threshold of signal energy check is usually decided by the quantization step to avoid errors caused by quantization in small energy blocks. Under the same consideration, the energy check can also be used when the audio compression is processed to increase the recovery accuracy rate. To achieve a better recovery accuracy rate when the audio compression is processed, a larger energy threshold can be assigned according to the step size of quantization and the characteristic of the compression algorithm.
5.4 Multiple-bit Echo Data Hiding
A high information transmission rate is a requirement of an audio watermarking technique. An audio file is usually shorter than ten minutes and the watermark information may be long, thus a sufficiently high information transmission rate is required for watermark embedding. The information transmission rate of embedding one bit of watermark into a single block seems a little lower than the required information rate.
The proposed modification of echo data hiding system tries to embed multiple bits of watermark into each block by representing the information with more than two digits. In this section, we considered about using the trinary and four-digit representation systems for the watermark data. The information transmission rate increases as more digits are used for watermark representation. The information transmission rate of embedding multiple watermark bits in a single block is illustrated in this section and is compared with the ordinary scheme, which embeds only one bit in each block.
The overall system performance not only considers the information transmission rate but also the recovery accuracy rate. However, there is a tradeoff between the number of embedding echo signal, which is decided by the digits used for watermark representation, and the recovery accuracy rate. In the end of this section, a most suitable watermark representation system is recommended.
For the watermark representation in the trinary system or the four-digit system, the recovery accuracy rates with varying echo magnitude, with varying watermark-embedding rate or with varying delay distance between the echo signals are examined in series. These experimental results are compared with each other. And Threshold with varying Wps
0 2 4 6 8 10 12
2 4 8 16 32 64 128 256
watermark-embedding rate
accuracy increase (%)
A=0.7, silence A=0.7, under 2 A=0.5, silence A=0.7, under 2
Fig. 34 Increase of accuracy rate after energy threshold check (varying watermark-embedding rate)
A=0.5, 0.7; Wps=2~256, step 2 time; d0=0.7, 0.8, 0.9msec, delay distance=0.6msec; energy threshold=1, 5.
the performance of binary watermark representation system, which was examined in prior sections, will be compared with the performances of the system of trinary and four-digit watermark representation.
The performance of the multiple-bit echo data hiding system should be the same trend as the single-bit scheme. Although the trends of performance are similar, the actual recovery accuracy rate of the trinary watermark representation system is lower than the binary watermark system; and the accuracy rate of the four-digit watermark representing system is still lower than the trinary scheme.
The recovery accuracy rate with varying echo magnitude of different watermark representation systems should be examined also.
The performance of different watermark representation systems with varying watermark-embedding rate and varied delay distance will be compared.
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