Multiresolution nonparametric regression and image denoising

Abstract

Recently new efficient algorithms, based on Lepski's approach, have been proposed in mathematical statistics for spatially adaptive varying scale denoising. A common feature of this sort of algorithms is that they form test-estimates different by the scale and special statistical rules are exploited in order to select the estimate with the best pointwise varying scale. In this paper a novel alternative multiresolution (MR) approach is proposed. Instead of selection of the estimate with the best scale a nonlinear estimate is built using all of the test-estimates. The estimation consists of two steps. The first step transforms the data into noisy spectrum coefficients (MR analysis). In the second step, these noisy estimates of the spectrum are filtered and used for estimation (MR synthesis). Simulation confirms an advance performance of the denoising algorithms based on the MR nonparametric regression.