By coupling the wavelet transform with a particular nonlinear shrinking function, the Red-telescopic optimal wavelet estimation of the risk (TOWER) method is introduced for removing noise from signals. It is shown that the method yields convergence of the L2 risk to the actual solution with optimal rate. Moreover, the method is proved to be asymptotically efficient when the regularization parameter is selected by the generalized cross validation criterion (GCV) or the Mallows criterion. Numerical experiments based on synthetic data are provided to compare the performance of the Red-TOWER method with hard-thresholding, soft-thresholding, and neighcoeff thresholding. Furthermore, the numerical tests are also performed when the TOWER method is applied to hard-thresholding, soft-thresholding, and neighcoeff thresholding, for which the full convergence results are still open.
Convergence of the Red-TOWER Method for removing noise from data
Amato U;
2001
Abstract
By coupling the wavelet transform with a particular nonlinear shrinking function, the Red-telescopic optimal wavelet estimation of the risk (TOWER) method is introduced for removing noise from signals. It is shown that the method yields convergence of the L2 risk to the actual solution with optimal rate. Moreover, the method is proved to be asymptotically efficient when the regularization parameter is selected by the generalized cross validation criterion (GCV) or the Mallows criterion. Numerical experiments based on synthetic data are provided to compare the performance of the Red-TOWER method with hard-thresholding, soft-thresholding, and neighcoeff thresholding. Furthermore, the numerical tests are also performed when the TOWER method is applied to hard-thresholding, soft-thresholding, and neighcoeff thresholding, for which the full convergence results are still open.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
