Thresholding of Wavelet Coefficientsas Multiple
نویسندگان
چکیده
Given noisy signal, its nite discrete wavelet transform is an estimator of signal's wavelet expansion coeecients. An appropriate thresholding of coeecients for further reconstruction of de-noised signal plays a key-role in the wavelet decomposition/reconstruction procedure. DJ1] proposed a global threshold = p 2 logn and showed that such a threshold asymptotically reduces the expected risk of the corresponding wavelet estimator close to the possible minimum. To apply their threshold for nite samples they suggested to always keep coeecients of the rst coarse j 0 levels. We demonstrate that the choice of j 0 may strongly aaect the corresponding estimators. Then, we consider the thresholding of wavelet coeecients as a multiple hypotheses testing problem and use the False Discovery Rate (FDR) approach to multiple testing of BH1]. The suggested procedure controls the expected proportion of incorrectly kept coeecients among those chosen for the wavelet reconstruction. The resulting procedure is inherently adaptive, and responds to the complexity of the estimated function. Finally, comparing the proposed FDR-threshold with that xed global of Donoho and Johnstone by evaluating the relative Mean-Square-Error across the various test-functions and noise levels, we nd the FDR-estimator to enjoy robustness of MSE-eeciency.
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