Subband variance computation of homoscedastic additive noise in discrete dyadic wavelet transform

The paper deals with noise power variation that occurs when Discrete Dyadic Wavelet Transform (DDWT) is applied to signals affected by Wide Sense Stationary (WSS) additive white noise owing to the use of a non orthonormal expansion. An exact relationship between the noise variance in the original signal and the noise variance in the wavelet coefficients at a generic level is derived. This relationship is crucial in the application of wavelet thresholding for signal denoising to properly select the threshold in each subband.The paper deals with noise power variation that occurs when Discrete Dyadic Wavelet Transform (DDWT) is applied to signals affected by Wide Sense Stationary (WSS) additive white noise owing to the use of a non orthonormal expansion. An exact relationship between the noise variance in the original signal and the noise variance in the wavelet coefficients at a generic level is derived. This relationship is crucial in the application of wavelet thresholding for signal denoising to properly select the threshold in each subband