Machine-learning based fast unsupervised variational image decomposition for fringe pattern analysis

The unsupervised variational image decomposition (uVID) algorithm developed in our group allows for automatic, accurate and robust preprocessing of diverse fringe patterns. Classical VID was initially used for image denoising. Its tailoring for fringe pattern preprocessing was justified by clear advantage over other methods (e.g. Wiener or Gauss filters) in maintaining sharp edges and details of the image. Historically first fringe pattern dedicated three-component variational image decomposition model assumed the use of the shearlet algorithm to separate the information component (fringes) and noise and the Chambolle projection algorithm to separate the fringes and background. We noticed that this model is computationally complicated and the result strongly depends on the values of the algorithm's internal parameters, to be set manually. The uVID automatically introduces the parameters and stopping criterion for Chambolle's iterative projection algorithm. Nevertheless, determining the stopping criterion in each iteration is a severely time-consuming process, which is particularly important given the fact that in many cases thousands of iterations have to be calculated in order to obtain a satisfactory fringe pattern decomposition result. Therefore, the idea of using machine learning algorithms to classify fringe patterns according to the required number of Chambolle projection iterations has emerged. Thus, it is no longer required to determine the value of the stopping criterion in every iteration, but only in the area of the predetermined number of iterations. We showed that the calculation time is reduced on average by half by employing the machine-learning based acceleration. This way we made a progress in developing uVID algorithm features for real-time studies of dynamic phenomena, i.e., biological cell development investigated by fringe-based bio-interferometry methods.