Phase Retrieval via Matrix Completion

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover

Robotic Path Planning and Visibility with Limited Sensor Data

Abstract — Autonomous robotic systems (observers) equipped with range sensors must be able to discover their surroundings, in an initially unknown environment, for navigational purposes. We present an implementation of a recent environmentmapping algorithm [1] based on Essentially Non-oscillatory (ENO) interpolation [2]. An economical cooperative control tank-based platform [3] is used to validate our algorithm. Each vehicle on the test-bed is equipped with a flexible caterpillar drive, range sensor, limited onboard computing, and wireless communication. I