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. GTW is similar to SPIHT 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.