De-noising by thresholding operator adapted wavelets

Donoho and Johnstone (Ann Stat 26(3):879–921, 1998) proposed a method from reconstructing an unknown smooth function u from noisy data $u+\zeta by translating the empirical wavelet coefficients of u+\zeta towards zero. We consider the situation where the prior information on the unknown function u may not be the regularity of u but that of {\mathcal {L}}u where {\mathcal {L}} is a linear operator (such as a PDE or a graph...