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Wavelet-based image coders optimally represent smooth regions and isolated point singularities. However, wavelet coders are less adept at representing perceptually important edge singularities, and coding performance suffers significantly as a result. We propose a novel two-stage image coder framework based on modeling images as edge cartoons + textures. In stage 1, we infer and efficiently code the edge information from the image using a multiscale wedgelet decomposition. In stage 2, we code the residual, "edgeless" texture image using a standard wavelet coder. Our preliminary coder improves significantly over standard wavelet coding techniques in terms of visual quality.