Sharp Adaptation for Inverse Problems with Random Noise

  • Cavalier L
  • Published 2000


We consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems, in particular multivari-ate ones. We propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale (that includes el-lipoids with polynomially and exponentially decreasing axes) and, at the same time, satisses asymptotically exact oracle inequalities within any class of linear estimates having monotone non-decreasing weights. As application, we construct sharp adaptive estimators in the problems of deconvolution and tomography.


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@inproceedings{L2000SharpAF, title={Sharp Adaptation for Inverse Problems with Random Noise}, author={Cavalier L}, year={2000} }