Uncertainty quantification and inverse estimation by probabilistic generative models from the beginning of the data analysis. An example is a Fourier basis method for inverse estimation in scattering analysis of microscopy videos. It does not require specifying a certain range of Fourier bases and it substantially reduces computational cost via the generalized Schur algorithm. See the reference: Mengyang Gu, Yue He, Xubo Liu and Yimin Luo (2023),