Estimation of Non-Parametric Function Using Wavelet Transform
Publication Date : 30/01/2018
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The Wavelet has number of functions for the estimation of an unidentified function (signal or image) in noise. This paper provides non-parametric function estimation of denoise signals/images. Non-parametric function estimation aims to estimate or recover or denoise a function of interest, perhaps a signal, spectrum or image, that is observed in noise and possibly indirectly after some transformation, as in deconvolution. ‘Non-parametric’ signifies that no a priori limit is placed on the number of unknown parameters used to model the signal. Such theories of estimation are necessarily quite different from traditional statistical models with a small number of parameters specified in advance. Before wavelets, the theory was dominated by linear estimators, and the exploitation of assumed smoothness in the unknown function to describe optimal methods. Wavelets provide a set of tools that make it natural to assert, in plausible theoretical models, that the sparsity of representation is a more basic notion than smoothness, and that nonlinear thresholding can be a powerful competitor to traditional linear methods. Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the massive literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. Compare various estimators in a wide-ranging simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters.
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