Fast Gabor wavelet transform based on synthesis of Gabor spectrum using convolution of Gaussian
Takanobu Ishikawa, Ryosuke Takayama, Shuichi Arai · 2015
Gabor wavelet transform is often used in time-frequency analysis for non-stationary signals. However, the calculation of continuous wavelet transform including Gabor wavelet transform is very complex. Mallat algorithm in discrete wavelet transform is representative of a speeding-up method of wavelet transform, but we can't use this algorithm for the Gabor wavelet since the Gabor wavelet is a non-orthogonal wavelet. Some methods, which approximate the basis function to orthonormal function, have been proposed to solve this issue. However, approximate accuracy of each algorithm is low. In this paper, we focus on mathematical characteristics of a Gaussian which is used as a basis function, and propose a synthetic method of wavelet coefficients using Gabor spectra which are calculated using FFT. In addition, we discussed the synthetic accuracy and calculation complexity, then made it clear that we can reduce the calculation complexity to about 1/20 in regard to general CWT maintaining the desired accuracy.