Research On Signal Denoising Technology Based On Adaptive Lifting Wavelet Transform

In the real world all of the signals are noisy signals, and noise interference will result in the distortion or even thorough change in the original signal, so it becomes an important research subject that how to restore the original signal from the noisy signal so as to realize the isolation of signals and noises and se the letter and improve signal to noise ratio become improve the SNR. In this paper, in-depth study is performed regarding the issues involved in the denoising of noisy signals, and make several denoising methods based on lifting wavelet transform are raised. Below are the three signal denoising methods raised in this paper.There are several shortcomings of the traditional wavelet transform method for signal denoising: on the one hand, the signal is various, and the traditional single wavelet transform cannot meet the needs of signal diversity; on the other hand, it consumes a significant amount of system resources for traditional wavelet transform to perform time-frequency-time change on signals, considering its own structure. To address the above issues, the paper proposes a method based on adaptive lifting wavelet transform to conformation orthonormal wavelets libraries. This method could select the appropriate wavelet according to the characteristics of sampling signals, and apply it to signal denoising. The method has quite a few features: the wavelet libraries conformed meet the requirement of signal diversity; the wavelet transform conformed based on adaptive lifting performs analysis of signals only on time-domain signal, which decreases the computation substantially; the conformation based on adaptive lifting has excellent representation in enhancing flexibility, real-time and adaptability.The typical lifting method divides the signal process into three stages: decomposition, forecasts and updates. In the original forecast is to calculate the design parameter in the operator by deriving polynomial. The parameter is obtained through adaptive algorithm. The method separates the operator parameter design and adaptive algorithm completely, and make them independent with each other. In such conditions, Kalman adaptive forecast algorithm, put forward in the article, represents good flexibility and simple operation. Kalman forecast algorithm could adjust parameter adaptively in the process of signal forecast to gain matrix parameters, making the prediction error meet the Minimum Mean Square Error Approach (MMSE). This method combines forecast and adaptivity organically, and reduces the computation significantly in the process of real-time signal analysis.There are different characteristics of the original threshold denoising method. Hard-threshold function has good performance in retaining the partial features of signal edge and in denoising mutant signals. Soft-threshold function is more smooth, however could lead to distortion such as vague signal edge. To balance the strength of hard-threshold and soft-threshold, the paper raises a half soft-threshold denoising method. For half soft-threshold function, there is a smooth transition area between noises and signals, which make it more coincident in continuity of natural signals or images.The simulations and experiments in the paper have indicated the effectiveness of the above methods.