| 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, and optical communication systems. The loss of information, caused for example by the evanescent waves that 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. that 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. The sparse inverse problems previously considered have usually been linear, however in optics many inverse problems are fundamentally nonlinear, due to the loss of phase information. We therefore developed methods for finding sparse solutions to nonlinear (quadratic) equations.
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, sub-wavelength imaging with partially incoherent illumination, and communication through a coupled waveguide array. |
