Logo of the phase retrieval challenge web site.

Follow the link to find out about phase retrieval. Two of the panels in the logo show the Fourier transform of the greek symbol phi: modulus on a gray scale, phase in color (as in a color wheel).

The challenge of phase retrieval is to recover phases from Fourier modulus data and general assumptions about the nature of the object (positivity, atomicity, ...). Sophisticated algorithms for phase retrieval have evolved in imaging, microscopy, and crystallographic applications. In spite of qualitative differences in the objects studied, the leading algorithms in these diverse fields share some key characteristics that are only poorly understood. One goal of the challenge web site is to promote the exchange of ideas between groups that have in the past worked independently. In addition, by offering challenge problems in the simplest and most clearly defined settings, it is hoped that workers outside the traditional fields can be attracted as well. For example, the problem of bit retrieval has close connections with factorization and combinatorial optimization, and yet is just one limit of the phase retrieval practiced by crystallographers.