Robust Image Coding Using the Embedded Zertotree Wavelet Algorithm

In this work, we present a new family of image compression algorithms derived from Shapiro’s embedded zerotrce wavelet (EZW) coder. These new algorithms introduce robustness to transmission errors into the bit stream while still preserving its embedded structure. This is done by partitioning the wavelet coefficients into groups, coding each group independently, and interleaving the bit streams for transmission-thus, if one bit is corrupted, then only one of these bit streams will be truncated in the decoder. If each group of wavelet coefficients uniformly spans the entire image, then the objective and subjective qualities of the reconstructed image can be very good even when an error occurs. To illustrate the advantages of this new family, we compare the performance of some of its members to that of the conventional EZW coder. For example, one of the robust variations has a peak signal to noise ratio (PSNR) slightly lower than the conventional algorithm when no errors occur (-0.12 dB for lena and -0.5 dB for barbara, both coded at 1.0 bits/pixel), but when a single error occurs at bit 1000, the PSNR of the new coder is more than 5 dB higher for both test images. The PSNR versus the bit error position is shown in Figure 1 using two different partitionings of the wavelet coefftcients and four interleaved bit streams. Using more interleaved bit streams increases robustness (i.e., more errors can be tolerated with less degradation) at the expense of reduced error-free rate-distortion performance. Finally, we note that the new algorithms do not increase the complexity of the overall system and, in fact, that they are far more easily parallelized than the conventional EZW coder.