Thresholding of Wavelet Coefficients as Multiple Hypotheses Testing Procedure

Given noisy signal, its finite discrete wavelet transform is an estimator of signal's wavelet expansion coefficients. An appropriate thresholding of coefficients for further reconstruction of de-noised signal plays a key-role in the wavelet decomposition/reconstruction procedure. [DJ1] proposed a global thresholdbackslashlambda = backslashsigma backslashsqrt 2backslashlog n 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 finite samples they suggested to always keep coefficients of the first coarse j0 levels.