ABSTRACT
One of the main problems we consider in this book is the estimation of a function from finitely many values of its Fourier transform. In such cases, the data are complex numbers and the function to be estimated is a complex-valued function. As we mentioned previously, there are certain cases in which we have a phase problem, where it is not possible to measure the complex numbers, but only their magnitudes. Estimating the structure of a crystal from scattering data in x-ray crystallography and optical imaging through a turbulent atmosphere are two examples in which the phase problem arises. As you might imagine, reconstruction from magnitude-only data is more difficult than from the full complex data.
