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Recently, new efficient algorithms, based on Lepski's approach , have been proposed for spatially adaptive varying scale de-noising. Special statistical rules are exploited in order to select the estimate with the best point-wise varying scale h from a set of test-estimates yˆh(x),h∈H. In this paper, a novel multiresolution (MR) nonparametric regression technique is developed. The adaptive algorithm consists of two steps. The first step transforms the data into noisy spectrum coefficients (MR analysis). In the second step, these noisy spectrum is filtered by the thresholding procedure and exploited for estimation (MR synthesis). This nonlinear estimate is built using the test-estimates yˆh(x) of all scales. Simulation confirms the advanced performance of the new de-noising algorithms based on the MR nonparametric regression.
Date of Publication: Oct. 2004