Modified variational image decomposition algorithm aided by the Hilbert transform as an alternative to 2D Hilbert-Huang transform for fringe pattern phase retrieval

Abstract

The process of information recovering from fringe pattern can be divided into two main parts: filtration (fringe pattern background and noise removal) and phase (or amplitude) demodulation. In recent years the 2D Hilbert spiral transform (HST) has become one of the most popular phase demodulation techniques. Together with empirical mode decomposition used for fringe pattern preprocessing forms a strong fringe pattern analysis algorithm called 2D HilbertHuang transform (HHT). Variational image decomposition was recently adapted for fringe pattern filtration. In combination with the 2D Hilbert spiral transform and after some modifications it might become an excellent tool for fringe pattern analysis purpose and can compete with well-developed HHT. Proposed modification is the first attempt to automate the variational image decomposition in terms of fringe pattern filtration. Received results show that VID-HST can compete with HHT and may become an excellent alternative for fringe pattern evaluation. Another fact encouraging the development of VID is a wide range of applications that have been proposed up to now, i.e., image denoising, fringe pattern filtration and phase filtration.