Improving speed and precision of local frequency analysis using Gaussian ridge interpolation for wavelet and windowed Fourier ridge algorithms

When analysing fringe images, wavelet and windowed Fourier ridge algorithms allow to extract phase and local frequency even in the presence of considerable noise levels. However, the precision of the local frequency information is often limited by the relatively small number of analysing frequencies used in practice. This on account of the direct trade-off between frequency precision and processing time, which can become prohibitive in some cases. In the present paper, a method is shown capable of reducing the processing time by a factor 3 for the wavelet ridge technique and by up to 15 times for the windowed Fourier ridge algorithm. This is accomplished by a 3-point Gaussian ridge interpolation. This approach is also shown to lead to an improved frequency precision for moderate noise levels. (c) 2015 Elsevier Ltd. All rights reserved.