On a Remarkable Property of Phase-Closure Imaging: Generalized Inverse via Backprojection Mechanisms

The phase-restoration procedure, which is a key element in solving the inverse problems of aperture synthesis, can be decomposed into two main stages. The first one is characterizing the space of solutions resulting from the phase-closure data; the second amounts to localizing the final solution in this space by taking into account additional constraints. Although these problems are closely imbricated, as revealed by the hybrid approaches [1], it is essential to examine them separately to clarify the analysis. This should help in defining the optimal method to be implemented in each particular situation. All the elements presented in this paper appear in the general framework of what may be called spectral extrapolation in phase-closure imaging. As shown in Refs. [2-4], the compromise to be found between resolution and robustness requires a good understanding of the inverse problems encountered in this field. In this paper, we simply propose a new formulation of the algebraic properties of phase-closure imaging, and outline some algorithmic implications concerning the first stage of the phase-restoration procedure.