arXiv:1509.00888 FOURIER PHASE RETRIEVAL WITH A SINGLE MASK BY THE DOUGLAS-RACHFORD ALGORITHM
نویسنده
چکیده
Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence. Since a single oversampled coded diffraction pattern is not enough to guarantee uniqueness of fixed point, the extra information and data needed takes either of the following two forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded.
منابع مشابه
Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm
Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence.
متن کاملFourier phase retrieval with a single mask by Douglas-Rachford algorithms.
The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded. Fo...
متن کاملFourier phasing with phase-uncertain mask
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in meas...
متن کاملMini - symposia Computational Inverse Scattering Problems and Applications in Imag - ing ( MS I - 1 , MS I -
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this talk Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measu...
متن کاملA New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs
In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas-Rachford splitting, or equivalently ADMM. When an optimization program is infeasible, unbounded, or pathological, the iterates of Douglas-Rachford splitting diverge. Somewhat surprisingly, such divergent iterates still provide useful information, which our method uses for i...
متن کامل