Wavelet decomposition approaches to statistical inverse problems

  title={Wavelet decomposition approaches to statistical inverse problems},
  author={Felix Abramovich and Bernard W. Silverman},
SUMMARY A wide variety of scientific settings involve indirect noisy measurements where one faces a linear inverse problem in the presence of noise. Primary interest is in some function f(t) but data are accessible only about some linear transform corrupted by noise. The usual linear methods for such inverse problems do not perform satisfactorily when f(t) is spatially inhomogeneous. One existing nonlinear alternative is the wavelet-vaguelette decomposition method, based on the expansion of the… 

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