To ensure that the embedding may not change the features of AMBTC, we first use the authentication index and position index to generate the position code where the authentication data is embedded into.
In the proposed scheme, we embed an eb-bit watermark consists of the authentication data into each AMBTC compressed image block.
Based on definitions of AMBTC, the quantization level a is smaller than quantization level b.
Table 1 shows the PSNR values for the six test images compressed by the AMBTC algorithm with blocks of size 2 x 2, 4 x 4, and 8 x 8.
In the future, we will try to propose an adaptive image authentication scheme for AMBTC compressed images, which can offer high quality for AMBTC compressed images with different block sizes.
In addition, the AMBTC scheme was used to compress the original images.
Table 1 shows the visual qualities of images obtained by the AMBTC scheme  with three different values of n, i.e., 2, 4, and 8.
The experimental results show that our scheme obtained better visual quality of the embedded images than Hu et al.'s scheme irrespective of the size of blocks used in the AMBTC compression technique.
For a smooth block [x.sub.i] whose absolute distance between [a.sub.i] and [b.sub.i] is small, its bitplane [p.sub.i] will be less significant in the AMBTC reconstruction process.
If the watermark bit to be embedded [w.sub.i]=0, then the AMBTC is used to encode the block [x.sub.i] by replacing the pixels that are not less than the mean value [m.sub.i] with the high mean [b.sub.i] and replacing the pixels that are smaller than the mean value [m.sub.i] with the low mean [a.sub.i].
Step 2: Each image block [x.sub.i] (or [y.sub.i]) is encoded by AMBTC, obtaining its mean value [m.sub.i] and its two quantization levels [a.sub.i] and [b.sub.i].
From these results we can see that the proposed algorithm is fragile to most attacks except for the change in brightness which is caused by the AMBTC's special ability in preserving the mean value and the first absolute central moment.