Coherent Diffractive Imaging (CDI) is an algorithmic imaging technique where intricate features are reconstructed from measurements of the freely diffracting intensity pattern. An important goal of such lensless imaging methods is to study the structure of molecules that cannot be crystallized. Ideally, one would want to perform CDI at the highest achievable spatial resolution and in a single-shot measurement such that it could be applied to imaging of ultrafast events. However, the resolution of current CDI techniques is limited by the diffraction limit, hence they cannot resolve features smaller than one half the wavelength of the illuminating light. Here, we present sparsity-based single-shot subwavelength resolution CDI: algorithmic reconstruction of subwavelength features from far-field intensity patterns, at a resolution several times better than the diffraction limit. This work paves the way for subwavelength CDI at ultrafast rates, and it can considerably improve the CDI resolution with X-ray free-electron lasers and high harmonics.

This work evaluates the importance of approximate Fourier phase information in the phase retrieval problem. The main discovery is that a rough phase estimate (up to π/2 rad) allows development of very efficient algorithms whose reconstruction time is an order of magnitude faster than that of the current method of choice--the hybrid input-output (HIO) algorithm. Moreover, a heuristic explanation is provided of why continuous optimization methods like gradient descent or Newton-type algorithms fail when applied to the phase retrieval problem and how the approximate phase information can remedy this situation. Numerical simulations are presented to demonstrate the validity of our analysis and success of our reconstruction method even in cases where the HIO algorithm fails, namely, complex-valued signals without tight support information.

Abstract-We propose a new "Mark-Ant-Walk" algorithm for robust and efficient covering of continuous domains by antlike robots with very limited capabilities. The robots can mark places visited 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 information besides that mentioned above. 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. In addition we demonstrate various benefits of our successive visits of the robot at the same location, that makes it suitable for patrolling.Finally we provide a new theoretical bound on covering time of a wide family of such mark and walk algorithms.

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