Abstract - Many of the limitations of optical microscopy and information processing are essentially the result of information loss. Such is the case in sub-wavelength imaging, ultra-fast pulse measurement, or optical communication systems. The loss of information, caused for example the evanescent waves which do not reach the microscope objective, or by the finite bandwidth of pulse measurement devices, or simply by a low signal to noise ratio - makes these problems mathematically ill-posed.
Our group has recently suggested that, under certain conditions, prior knowledge about the sought information may be used in order to regularize such optical problems as those mentioned above. This is particularly true if the information can be represented compactly in a known representation, i.e. it is sparse in a known basis. The use of sparsity in solving inverse signal-processing problems has become very popular in recent years, with applications including fast medical imaging, fast radar and many more.
This talk will review several theoretical and experimental applications of sparsity to recovering information that was lost due to limits of the measurement device, such as sub-wavelength lensless imaging, phase retrieval, and sub-wavelength imaging with partially incoherent illumination.
Bio - Yoav Shechtman is a final-year PhD student in the group of Mordechai Segev, in the Physics department at the Technion, Israel Institute of Technology. He holds a BSc in Physics and a BSc in Electrical Engineering from the Technion. He is the author of a number of publications on optical information processing, which have appeared in Optics Letters, Optics Express and Nature Materials.