A ridge extraction algorithm based on partial differential equations of the wavelet transform

For the disadvantages of traditional ridge extraction algorithms based on the modulus maxima and phase information of wavelet coefficients, this paper proposes a new ridge extraction algorithm based on partial differential equations of the wavelet transform. According to the relationship between wavelet ridge and the modulus maxima of wavelet coefficients, the initial position of ridge is determined, and iterative formula of wavelet parameters is derived for determining other ridge points. After calculating all the wavelet coefficients at the initial time, the starting position of the ridge is chosen by searching the maximum value of these wavelet coefficients, then a complete ridge will be fitted through several ridge points obtained by successive iteration using the derived iterative formula. The biggest advantage of this algorithm is that it does not need to calculate the entire wavelet transform time-frequency plane, so redundant computation is avoided. Experimental results show that the computing speed has been significantly improved compared with Carmona´s Crazy-Climber algorithm. The extracted wavelet ridges can accurately restore effective frequency components of signals. Signals can be reconstructed by their ridges and the noise signals are removed. This algorithm is especially suitable for wavelet ridge extraction of multi frequency component asymptotic signals.