RECONSTRUCTION OF COMPLEX SIGNALS FROM INTENSITIES OF FOURIER-TRANSFORM PAIRS

The problem of retrieving a complex function when both its square modu lus and the square modulus of its Fourier transform are known is consi dered. When these intensities are directly assumed to be data, it amou nts to performing the inversion of a quadratic operator. The solution is found to be the global minimum of an appropriate functional. Moreov er, inasmuch as the unknown function is modeled within a finite-dimens ional set, the data are also consistently represented within finite-di mensional subspaces, and a coherent discretization of the problem resu lts. Because the assumed formulation involves nonquadratic functionals , the crucial problem of the existence of local minima in the course o f the minimization procedure is discussed. The main factors affecting these minima can be identified, such as the amount of available indepe ndent data. Furthermore, quadraticity makes it possible to define an e fficient conjugate-gradient-based minimization procedure. The numerica l results confirm the distinguishing feature of the proposed approach- its ability to obtain the solution starting from a completely random g uess. (C) 1996 Optical Society of America.