Summary form only given. This paper describes an adaptive error recovery technique for a DWT-based coding and transmission system, which recovers singularity information as well as continuity. The approach provided in this paper not only interpolates from the boundary, but also maintains the sharpness in background instead of smoothing the discontinuity out. The recovery function is modeled by the numerical solution of a special category of elliptic equation. The difference between adjacent data can be adjusted by the given weights. The choice of the weights allows high flexibility in maintaining contrast, since we can give small weights where we have evidence for edges.