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This paper introduces a new framework for error concealment in block-based image coding systems: sequential recovery. Unlike previous approaches that simultaneously recover the pixels inside a missing block, we propose to recover them in a sequential fashion such that the previously-recovered pixels can be used in the recovery process afterwards. The principal advantage of the sequential approach is the improved capability of recovering important image features brought by the reduction in the complexity of statistical modeling, i.e., from blockwise to pixelwise. Under the framework of sequential recovery, we present an orientation adaptive interpolation scheme derived from the pixelwise statistical model. We also investigate the problem of error propagation with sequential recovery and propose a linear merge strategy to alleviate it. Extensive experimental results are used to demonstrate the improvement of the proposed sequential error-concealment technique over previous techniques in the literature.