This paper describes an approach to coherent aperture synthesis and fine-resolution image reconstruction employing phase retrieval from intensity measurements. A Gerchberg-Saxton algorithm is used on a pair of intensity measurements to obtain the fields for each telescope at each position of the telescopes without a reference beam. These are combined into a larger synthetic aperture, and a cros...

Phase retrieval seeks to recover a signal x ∈ C from the amplitude |Ax| of linear measurements Ax ∈ C. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut) similar to the classical MaxCut semidefinite program. We solve this problem using a provably convergent block coordinate descent algorithm wh...

The wave aberration of human eyes is retrieved from actual point-spread-function (PSF) data and the modulus of the pupil function. The PSF had been obtained previously by application of a hybrid optical-digital method developed recently. The retrieval is done by using a bidimensional Gerchberg-Saxton phase-retrieval algorithm joined to an iterative phase-unwrapping algorithm. To obtain an adequ...

In this paper, we present infinitely many conserved densities satisfying particular conservation law $F_{t}=(2uF)_{x}$ for the generalized Riemann equations at $N=2,3,4$. $N=2$ case, also construct corresponding to new laws containing an arbitrary smooth function. virtue of reductions and/or changes variables, related are obtained two component Hunter-Saxton equation, Gurevich-Zybin equation an...