Bayesian Approach for Inverse Problems in Optical Coherent and Non Coherent Imaging

摘要

In many applications of optical imaging or diffraction scattering (ultrasounds or microwave), one of the main mathematical part of the inversion, problems, when linearized, become a Fourier synthesis (FS) one. This problem consists in estimating a multivariable function from the measured data which correspond to partial knowledge of its Fourier transform (FT). Most classical methods of inversion are based on interpolation of the data and fast inverse FT. But, when the data do not fill uniformly the Fourier domain or when the phase of the signal is lacking as in optical interferometry, the results obtained by such methods are not satisfactory, because these inverse problems are ill-posed. The Bayesian estimation approach, via an appropriate modeling of the unknowns gives the possibility of compensating the lack of information in the data, thus giving satisfactory results. In this paper we give an example of FS problem in an interferometry imaging.