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In this paper, the problem of concealing missing image blocks is casted into a framework of Bayesian estimation. The conditional expectation of the missing block vector is taken over a pilot vector of correctly decoded pixels near the missing block. Multiple observations of the missing vector and pilot vectors obtained in a neighborhood are used to approximate the expectation. We design a multiscale estimation approach with discrete cosine transform pyramid to improve estimation efficiency. The DC image of the missing block is recovered first, and then more details related to high-frequency AC coefficients are recovered successively. Moreover, the algorithm operates in an iterative mode through using estimated block to refine the searching process for the next estimation. The algorithm is found to perform very well for a wide range of block loss rates. Substantial improvement over 14 existing error concealment (inclusive of inpainting) algorithms on various images is demonstrated in our extensive experiments, under different test conditions inclusive of high-loss rates and large block sizes.