Seminar Series

Phase problems


Prof Rick Millane


Department of Electrical and Computer Engineering, University of Canterbury

Time & Place

Fri, 19 May 2017 14:00:00 NZST in Kirkwood KH03


Diffraction imaging involves constructing an image of an object from measurements of a diffracted field. Applications include optical astronomy, biological imaging using electron or x-ray diffraction, tissue imaging using light or ultrasound, and microwave imaging. If the scattering is weak, the diffracted field is the spatial spectrum, or Fourier transform, of the object scattering function. Furthermore, if the wavelength is small, or the field propagates through a distorting medium, only the amplitude, but not the phase, of the diffracted field can be measured. Since the amplitude and phase of the spectrum are required to compute a reconstruction of the object (by inverse Fourier transformation), loss of the phase is referred to as a “phase problem.” Reconstruction of the object from amplitude-only information is referred to as “phase retrieval.”

Two aspects of fundamental importance for phase problems are uniqueness and reconstruction. Under what conditions is an object uniquely determined by the amplitude of its spectrum? Uniqueness depends on the object shape, the
dimensionality, and the sampling of the amplitude data. The problem of reconstructing an object from the amplitude of its spectrum is non-convex, and requires algorithms with good global convergence. Most practical reconstruction algorithms for objects with many degrees of freedom are based on iterated projections. In this talk, I will give an overview of uniqueness properties of phase problems, reconstruction algorithms, and some applications.