1、 1 A New Method of Robust Image Compression Based on the Embedded Zerotree Wavelet Algorithm Charles D. Creusere III. ROBUST EZW (REZW) ALGORITHM The basic idea of the REZW image compression algorithm is to divide the wavelet coefficients up into S groups and then to quantize and code each of them i
2、ndependently so that S different embedded bitstreams are created. These bitstreams are then interleaved as appropriate (e.g., bits, bytes, packets, etc.) prior to transmission so that the embedded nature of the composite bitstream is maintained. In the remainder of this paper we assume that individu
3、al bits are interleaved. For the REZW approach to be effective, each group of wavelet coefficients must be of equal size and must uniformly span the image. A similar method has been proposed in to parallelize the EZW algorithm, but that method instead groups the coefficients so that data transmissio
4、n between processors is minimized. What do we gain by using this new algorithm over the conventional one? As has been pointed out in Section II, the EZW decoder can use all of the bits received before the occurrence of the first error to reconstruct the image. By coding the wavelet coefficients with
5、 multiple, independent (and interleaved) bit streams, a single bit error truncates only one of the streams the others are still completely received. Consequently, the wavelet coefficients represented by the truncated stream are reconstructed at reduced resolution while those 2 represented by the oth
6、er streams are reconstructed at the full encoder resolution. If the set of coefficients in each stream spans the entire image, then the inverse wavelet transform in the decoder evenly blends the different resolutions so that the resulting image has a spatially consistent quality. IV. STOCHASTIC ANAL
7、YSIS To evaluate the effectiveness of this family of robust compression algorithms, we assume that the coded image is transmitted through a binary symmetric, memoryless channel with a probability of bit error given by . We would like to know the number of bits correctly received in each of the S str
8、eams. Since this quantity is itself a random variable, we use its mean value to characterize the performance of the different algorithms. Because the channel is memoryless, streams terminate independently of each other, but the mean values of their termination points are always the same for a specif
9、ied . Assuming that the image is compressed to B total bits and that S streams are used, then the probability of receiving k of the B/S bits in each stream correctly is given by BSkBSkkpkk)1(0)1()( (2) which is a valid probability mass function as one can easily verify by summing over all k: In (2),
10、 k)1( is the probability that the first k bits are correct while is the probability that the (k + 1)th bit is in error. Note that a separate term conditioned on B/S is necessary to take into account the 3 possibility that all of the bits in the stream are correctly received. The mean value can now b
11、e calculated as BSks kpkm0)( (3) On the average, the total number of bits correctly received is smS . If B/S is large relative to1/ , then 1mms . Generally, the gain actually achieved is not this high, but it is nonetheless significant. In Section V, we use (3) to analyze the impact of transmission errors on the average quality of the reconstructed image for all possible values of S.
