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In this paper, we present an adaptive maximum a posteriori (MAP) error concealment algorithm for dispersively packetized wavelet-coded images. We model the subbands of a wavelet-coded image as Markov random fields, and use the edge characteristics in a particular subband, and regularity properties of subband/wavelet samples across scales, to adapt the potential functions locally. The resulting adaptive MAP estimation gives PSNR advantages of up to 0.7 dB compared to the competing algorithms. The advantage is most evident near the edges, which helps improve the visual quality of the reconstructed images.