Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach

摘要: In this paper we compute the maxisets of some denoising methods (estimators) for multidimensional signals based on thresholding coefficients in hyperbolic wavelet bases. That is, determine largest functional space over which risk these estimators converges at a chosen rate. unidimensional setting, refining choice that are subject to by pooling information from geometric structures coefficient domain (e.g., vertical blocks) is known provide ‘large maxisets’. situation less straightforward. sense much more exposed curse dimensionality. However identify cases where has clear benefit. particular, general structural constraints can be related compound models and minimal level anisotropy.