Distortion-free boundary extension method for online wavelet denoising

A distortion-free boundary extension device for online wavelet denoising, comprising a distortion-free boundary extension module and a wavelet denoiser, wherein

• the distortion-free boundary extension module is used for performing a distortion-free boundary extension on an acquired signal segment to obtain M+N+L data, wherein M represents a number of historical data used for a distortion-free left extension;
• L represents a number of future data used for a distortion-free right extension;
• N represents a number of data to be denoised;
• the wavelet denoiser is used for decomposing a lifting wavelet of the N data to be denoised into j layers to acquire approximation coefficients sj and detail coefficients {dj, . . . , d2,d1}, calculating a threshold Tj of each layer of the lifting wavelet, thresholding the detail coefficients {dj, . . . , d2,d1} of each layer to obtain estimated values of the detail coefficients, performing wavelet reconstruction by the approximation coefficients sj and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal {circumflex over (x)}n after denoising, and outputting data.

An electronic device, comprising a memory, a processor and a computer program, wherein the computer program is stored in the memory, and the processor runs the computer program to execute the following steps:

• S1:
• acquiring a signal segment xn, and performing a distortion-free boundary extension on the signal segment to obtain M+N+L data, wherein M represents a number of historical data used for a distortion-free left extension;
• L represents a number of future data used for a distortion-free right extension;
• N represents a number of data to be denoised;
• S2:
• decomposing a lifting wavelet of the N data to be denoised into j layers according to the historical data and the future data to acquire approximation coefficients sj and detail coefficients {dj, . . . , d2,d1};
• S3:
• calculating a threshold Tj of each layer of the lifting wavelet;
• S4:
• thresholding the detail coefficients {dj, . . . , d2,d1} of each layer to obtain estimated values of the detail coefficients;
• S5:
• performing wavelet reconstruction by the approximation coefficients sj and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal {circumflex over (x)}n after denoising;
• and
• S6:
• outputting data.