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Detection of weak signals in non-Gaussian noise using nonlinear wavelet denoising

In this paper, we present a nonlinear suboptimal detector whose performance in the leptokurtic noise is significantly better than that of matched filter. This detector contains a denoising pre-processor based on a non-linear wavelet transform called median interpolating pyramid transform (MIPT) proposed by Donoho and Yu [1]. The output of the pre-processor is passed through a matched filter and a threshold detector to decide whether the signal is present. The performance analysis of this nonlinear wavelet denoising (NWD) detector has been done by deriving the relation between the PDF of denoised signal and the PDF of input signal. Thus the mean and the variance of the test statistic are determined to provide the receiver operating characteristic (ROC) of the NWD detector in the asymptotic case. The theoretical analysis, confirmed by the experimental results, shows a significant improvement in the performance of the proposed detector over that of the matched filter in non-Gaussian noise.