A Modified SPIHT Algorithm for Image Coding With a Joint MSE and ...

722 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 3, MARCJ 2006Fig. 13. Gaussian noise at 03 dB SNR is added to the finest LH waveletcoefficients of the right half texture, to obtain the synthetic textures shown inthe left half.Fig. 15. Gaussian noise at 03:5 dB SNR is added to the second-level LHwavelet coefficients of the right half texture, to obtain the synthetic texturesshown in the left half.Fig. 14.Classification errors as the function of MSE are compared amongMSPIHT ( = 50000), MSPIHT ( =0), and the original SPIHT. The bitrates are 0.2, 0.3, 0.4, 0.5, and 0.6 bpp. Results are shown for data in Fig. 13.As indicated above, there is potential for disturbance of zerotrees via the coefficient reweighting. This implies that the performanceof the MSPIHT algorithm may be impacted by whichparticular wavelet coefficients are scaled to be large (where inthe wavelet tree). In the pervious example the significant waveletcoefficients (for which noise was added) were at the finest level.We now consider a synthetic image as in the left half of Fig. 15,but now the white Gaussian noise is added to the coefficientsin the second LH band (for levels, as in the previousexample). In this case, the SNR, as defined above, is dB.Results are presented in Fig. 16. We again considerfor the MSPIHT results for which classification is emphasized.In Fig. 16, we note that MSPIHT for provides excellentclassification performance for low MSE (highest bpp), betterthan MSPIHT with . This is attributed to the factthat the coefficients that are important are relatively large inamplitude (lower scale than in Fig. 14). These large-amplitudeFig. 16.Classification errors as the function of MSE are compared amongMSPIHT ( = 50000), MSPIHT ( =0), and the original SPIHT. The bitrates are from 0.2 to 0.6 bpp at the interval of 0.05 bpp. Results are shown forsynthesized data in Fig. 15.coefficients, which are also important for classification arereconstructedwell by SPIHTand MSPIHT with . However,at lower bpp (higher MSE), the classification improvementof MSPIHT withis more evident. Note that inFig. 14, for which the small-amplitude finest-level coefficientsare important for classification, the MSPIHT withyields better classification performance for all MSE (bpp)considered.D. Modified SPIHT and Bayes VQThe Bayes tree-structured vector quantization (B-TSVQ) algorithmintroduced by Oehler and Gray [15] is a joint compressionand classification technique. It combines classification andcompression into a single vector quantizer by incorporating aBayes risk term into the distortion measure. For large block