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Phase Retrieval

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Abstract:
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. Phase retrieval is concerned with reconstructing an image of an object from measurements of only the amplitude of its spatial spectrum, and is referred to as a ``phase problem.’’

Two aspects of fundamental importance in 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 describe uniqueness properties of phase problems, including some recent results, and reconstruction algorithms.

Type of Seminar:
IfA Seminar
Speaker:
Prof. Rick Millane
Department of Electrical and Computer Engineering, University Canterbury, Christchurch, New Zealand
Date/Time:
Aug 06, 2015   16:15
Location:

ETZ E 6, Gloriastr. 35
Contact Person:

Prof. Smith
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Biographical Sketch:
Rick Millane is a Professor in the Department of Electrical and Computer Engineering at the University Canterbury in New Zealand. He received a PhD in EE at Canterbury and was on the academic staff at Purdue University in the US for 20 years. He returned to the University of Canterbury in 2001 and was Head of Department of ECE during 2008-2011. His research interests are in computational imaging and image reconstruction, with applications in biophysics, medical imaging, and Earth and atmospheric sciences. He is currently visiting at the Center for Free-electron Laser Science in Hamburg. Rick is a Fellow of the Optical Society of America, SPIE and IPENZ.