Eliyahu Osherovich, Oren Cohen, Yonina C. Eldar et al.
We present a novel method for Ankylography: three-dimensional structure reconstruction from a single shot diffraction intensity pattern. Our approach allows reconstruction of objects containing many more details than was ever demonstrated, in a faster and more accurate fashion
Eliyahu Osherovich
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction imaging (CDI). Our main goal is to develop an efficient reconstruction method based on continuous optimization techniques. Unlike current reconstruction methods, which are based on alternating projections, our approach leads to a much faster and more robust method. However, all previous attempts to employ continuous optimization methods, such as Newton-type algorithms, to the phase retrieval problem failed. In this work we provide an explanation for this failure, and based on this explanation we devise a sufficient condition that allows development of new reconstruction methods---approximately known Fourier phase. We demonstrate that a rough (up to $π/2$ radians) Fourier phase estimate practically guarantees successful reconstruction by any reasonable method. We also present a new reconstruction method whose reconstruction time is orders of magnitude faster than that of the current method-of-choice in phase retrieval---Hybrid Input-Output (HIO). Moreover, our method is capable of successful reconstruction even in the situations where HIO is known to fail. We also extended our method to other applications: Fourier domain holography, and interferometry. Additionally we developed a new sparsity-based method for sub-wavelength CDI. Using this method we demonstrated experimental resolution exceeding several times the physical limit imposed by the diffraction light properties (so called diffraction limit).
Eliyahu Osherovich
In this work we present an algorithm for covering continuous connected domains by ant-like robots with very limited capabilities. The robots can mark visited places with pheromone marks and sense the level of the pheromone in their local neighborhood. In case of multiple robots these pheromone marks can be sensed by all robots and provide the only way of (indirect) communication between the robots. The robots are assumed to be memoryless, and to have no global information such as the domain map, their own position (either absolute or relative), total marked area percentage, maximal pheromone level, etc.. Despite the robots' simplicity, we show that they are able, by running a very simple rule of behavior, to ensure efficient covering of arbitrary connected domains, including non-planar and multidimensional ones. The novelty of our algorithm lies in the fact that, unlike previously proposed methods, our algorithm works on continuous domains without relying on some "induced" underlying graph, that effectively reduces the problem to a discrete case of graph covering. The algorithm guarantees complete coverage of any connected domain. We also prove that the algorithm is noise immune, i.e., it is able to cope with any initial pheromone profile (noise). In addition the algorithm provides a bounded constant time between two successive visits of the robot, and thus, is suitable for patrolling or surveillance applications.