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Therefore, for the problem of hard threshold function and soft threshold function, we use an improved threshold function, which is defined as follows:
Here is the comparison curves between the improved threshold function and the soft and hard thresholding functions٬It can be observed that at point wavelet coefficient equals w, the improved threshold function overcomes the discontinuity at point in the hard thresholding function, and avoids oscillations during signal reconstruction. In segment The wavelet coefficient is greater than or equal to w, the improved threshold function more closely aligns with the hard thresholding function and does not exhibit the constant error observed in the soft thresholding function in this region.
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