# 18.12.4.1 Algorithms (Denoise)

The noisy signal is first decomposed into several sets of approximation coefficients and detail coefficients using multi-level 1D wavelet decomposition. Then all the detail coefficients whose absolute values are less than the threshold are discarded. Finally, the approximation coefficients and the altered detail coefficients are used to reconstruct the denoised signal.

Multi-level 1-D wavelet decomposition is a process of successively decomposing the approximation coefficients. Let nLevel denote the number of times the decomposition is performed. Then we can compute nLevel as: $nLevel=min(7,log_{2} N)$ ,

where N is the length of the input signal.

Thresholding is performed on only the detail coefficients of the last / levels, where / is specified by the Thresholding Level option. The values of these coefficients are then examined. And those whose absolute values are less than the threshold value will be replaced with zeros.

If the threshold type is sqtwolog, the threshold level will be computed by:$\sqrt {2\log _{10} N_{cd} }$

where $N_{cd}$ is the number of detail coefficients of the last /levels.