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...

We describe a unique approach for extracting the temporal profile of ultrashort laser pulses from typical autocorrelation measurements. The use of the constraint that intensity is a nonnegative quantity enables an iterative numerical algorithm to reconstruct pulse shapes in a one-dimensional procedure. With the reconstruction of the intensity profile, the Gerchberg–Saxton algorithm can be used ...

Abstract. The Papoulis-Gerchberg (PG) algorithm is well known for band-limited signal extrapolation. The authors consider the generalization of the PG algorithm to signals in the wavelet subspaces in this research. The uniqueness of the extrapolation for continuous-time signals is examined, and sufficient conditions on signals and wavelet bases for the generalized PG (GPG) algorithm to converge...