Compressive sensing is a class of image recovery techniques utilizing sparsity priors to recover undersampled signals with high fidelity. This talk is about compressive sensing for phase retrieval from coherent fields and correlation function retrieval from partially coherent fields. For coherent fields, I will discuss in particular the use of intensity priors in the “transport of intensity equation” method, where the phase
is obtained by analogy to a lateral pressure potential in a compressible flow. Transport of intensity is especially interesting in the x-ray regime, where standard interferometry is difficult because common sources are spatially partially coherent and beam splitters-combiners are not available; as a convincing example, I will show how the sparsity prior of quasi-constant object density allows successful x-ray
phase recovery despite the low coherence. For partially coherent fields, I will describe how the use of phase-space (Wigner space) methods and sparsity priors on the number of coherent modes allow the retrieval of the correlation function, which can still lead to complete characterization of physical objects.

»ã±¨È˼ò½é£ºGeorge Barbastathis: received the Diploma in Electrical and Computer Engineering in 1993 from the National Technical University of Athens (Πολυτεχνε?ο) and the MSc and PhD degrees in Electrical Engineering in 1994 and 1997, respectively, from the California Institute of Technology (Caltech.) After post-doctoral work at the University of Illinois at Urbana-Champaign, he joined the faculty at MIT in 1999, where he is now Professor of Mechanical Engineering and holds the Singapore Research Professorship in Optics. He has worked or held visiting appointments at Harvard University, the Singapore-MIT Alliance for Research and Technology (SMART) Centre, the National University of Singapore, and the University of Michigan – Shanghai Jiao Tong University Joint Institute (ÉϺ£½»Í¨´óѧÃÜÎ÷¸ù´óѧѧԺ) in Shanghai, People’s Republic of China.. His research interests are threedimensional and spectral imaging; phase estimation; and gradient index optics theory and implementation with subwavelength-patterned dielectrics. He is member of the Institute of Electrical and Electronics Engineering (IEEE), the American Society of Mechanical Engineers (ASME) and in 2010 he was elected Fellow of the Optical Society of America.