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This paper presents group testing for wavelets (GTW), a novel embedded-wavelet-based image compression algorithm based on the concept of group testing. We explain how group testing is a generalization of the zerotree coding technique for wavelet-transformed images. We also show that Golomb coding is equivalent to Hwang's group testing algorithm (Du and Hwang 1993). GTW is similar to SPIHT (Said and Pearlman 1996) but replaces SPIHT's significance pass with a new group testing based method. Although no arithmetic coding is implemented, GTW performs competitively with SPIHT's arithmetic coding variant in terms of rate-distortion performance.