Ridges reconstruction based on inverse wavelet transform

Ridges always carry important physical information in practice. Ridge reconstruction based on inverse wavelet transform is studied in this article. It is emphasized that the points within the neighbor area have to be added in the reconstruction to avoid energy lost. However, no discussion has been proposed about how to choose the neighbor area up to now although it is the key to achieve good performance. A formula is given in this article to calculate the width of the neighbor area, which varies with scale and the signal itself. Some examples are given in this article to show the performance of the proposed method, which manifests that the method works very well for signals with multiple components as long as there is no cross section between them. It also works well when the signal to noise ratio is not very low.