Signal Denoising based on Dual Tree Complex Wavelet Transform and Goodness of Fit Test

We proposes a signal denoising framework algorithm which employs goodness of fit (GOF) test on complex wavelet coefficients obtained via dual tree complex wavelet transform (DT-CWT). Owing to its redundancy, DT-CWT is near translation invariant insuring better denoising performance over the classical discrete wavelet transform (DWT). The GOF test is used to identify the noisy DT-CWT coefficients whereby statistics based on empirical distribution function (EDF), namely Anderson Darling (AD) statistics, is employed to quantify the distance between the EDFs of local wavelet coefficients and reference white Gaussian noise (WGN) distribution. We pose the denoising as a hypothesis testing problem where null hypothesis corresponds to detection of noise while alternate hypothesis corresponds to the signal detection. Experimental results demonstrate that the proposed signal denoising method gives superior performance over the state of the art methods.