Digital Signal Denoising Based On Wavelet Tansform And Threshold Functions

Since the beginning of wavelet transform in signal processing, it has been noticed that wavelet thresholding is of considerable interest for removing noise from signals. Recently, Donoho and others have presented the soft-thresholding and the hard-thresholding. Several years later, compromise function and modulus squared function are also proposed. Certainly, they have their own advantageit to denoise the white noise. But all of them have a disadvantage: they can not smooth the impulsive noise effectively though they can do the white Gaussian noise.It is well known that 8 function can simulate the impulsive noise and have its own nature. For the disadvantage of the conversational thresholding functions, thispaper proposes the modification to them, firstly, let u_j,k = then addanother condition to the conversational thresholding functions, that is to say, we judge not only the relation of the value |ω_j,k| and the threshold but also the relation of thevalue |u_j,k| and the threshold. Theoretically, four modified thresholding functions areproved to be effective to denoise the impulsive noise. Simulations also show that four modified thresholding functions are all effective not only to denoise the white Gaussian noise but also to the impulsive noise.