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This talk concerns estimation for the deconvolution problem over the real line.New algorithms are developed for this nonstandard deconvolution problem and it is shown that these new estimators attain the lower bound minimax, and hence optimal, rate of convergence.Our method has applications to such problems as the deblurring of optical images which have been subjected to uniform motion over a finite interval of time.We also treat the case when the support of the uniform is not given and must be estimated.The numerical properties of our algorithms are demonstrated and shown to be well behaved.This is joint work with P.Kim and J.Sun.