Authors Address the problem of recognition and retrieval of relatively weak industrial signal such as Partial Discharges (PD) buried in excessive noise. The major bottle-neck being the recognition and suppression of stochastic pulsive interference (PI) which has similar frequency characteristics as PD pulse. Also, the occurrence of PI is random like PD pulses. In this paper we provide techniques to de-noise, detect, estimate and classify the PD signal in a statistical perspective. To avoid aliasing due to interference of high frequency noise, PD signals are generally digitized in much higher sampling rates (in terms of tens of MHz), than actually required. A multi-resolution analysis based technique is incorporated to discard the huge amount of redundant data in acquired signal. A scale dependent MMSE based estimator is implemented in undecimated wavelet transform (UDWT) domain to enhance the noisy signal, due to its inherent advantages offered in the analysis of PD signal. The probability density function of the enhanced signal is derived using probabilistic principal component analysis (PPCA) in which PD/PI pulses are modeled as mean of the distribution. The parameters of the pulses are estimated using maximum aposteriroi probability (MAP) based technique. A statistical test known as generalized log likelihood ratio test (GLRT) was incorporated to ensure the existence of the pulse. The decision as to whether a pulse is a noise or a desired signal has been made based on a weighted-nearest neighbor methodology.