Abstract
Making use of the advantages of the soft and hard threshold methods proposed by Donoho, this paper presents a deviation variable based on quadratic polynomial and differentiable improvement function, according to the characteristics of the underground water pipe leakage signal. In the paper we constructed the mathematical model of the function, utilized wavelet de-noising algorithm for the collected ultrasonic signal de-noising, compared the de-noising effect by means of the value of Signal to Noise Ratio (SNR) and Mean Squared Error (MSE). Results show that the new function has the better de-noising effect compared with the original threshold function.
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