scholarly journals Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Nguyen Hieu Thao ◽  
Oleg Soloviev ◽  
Michel Verhaegen
Keyword(s):  
Numerical Analysis ◽  
Convergence Analysis ◽  
Phase Retrieval ◽  
Convex Combination ◽  
Projection Methods ◽  
The Other ◽  
Convergence Criteria ◽  
Alternating Projection ◽  
Retrieval Problem ◽  
Mathematical Characteristics

AbstractWe present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical characteristics of the phase retrieval problem. Numerical results demonstrate the advantages of the algorithm over the other widely known projection methods in practically relevant simulations.

scholarly journals Projection methods for high numerical aperture phase retrieval

2021 ◽  
Author(s):  
Hieu Thao Nguyen ◽  
Oleg Soloviev ◽  
D Russell Luke ◽  
Michel Verhaegen
Keyword(s):  
Phase Retrieval ◽  
Numerical Aperture ◽  
Projection Methods ◽  
The Other ◽  
Projection Operators ◽  
Mathematical Framework ◽  
Convergence Criteria ◽  
Projection Algorithms ◽  
High Numerical Aperture ◽  
Retrieval Problem

Abstract We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.

scholarly journals Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rujia Li ◽  
Liangcai Cao
Keyword(s):  
Phase Retrieval ◽  
Dynamic Range ◽  
A Priori ◽  
Measured Intensity ◽  
Physical Constraints ◽  
Coherent Diffraction Imaging ◽  
Effective Dynamic ◽  
Ill Posed ◽  
Retrieval Problem ◽  
Diffraction Imaging

AbstractPhase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

The Numerical Analysis of the Velocity and Pressure Distribution of the Oil Film in Heavy Hydrostatic Thrust Bearing

2014 ◽  
Vol 541-542 ◽  
pp. 658-662
Author(s):  
Jian Li ◽  
Yuan Chen ◽  
Yang Chun Yu ◽  
Zhu Xin Tian ◽  
Yu Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Pressure Distribution ◽  
Working Conditions ◽  
Thrust Bearing ◽  
Rotation Speed ◽  
The Other ◽  
Surface Load ◽  
Oil Film ◽  
Volume Method

To study the velocity and pressure distribution of the oil film in a heavy hydrostatic thrust bearing, a mathematical model of the velocity is proposed and the finite volume method (FVM) has been used to simulate the flow field under different working conditions. Some pressure experiments were carried out and the results verified the correctness of the simulation. It is concluded that the pressure distribution varies small under different rotation speed when the surface load on the workbench is constant. But the velocity of the oil film is influenced greatly by the rotation speed. When the rotation speed of the workbench is as quick as enough, the velocity of the oil film on one radial side of the pad will be zero, that is to say the lubrication oil will be drained from the other three sides of the recess.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

SPECTRAL APPROXIMATION OF A SCHRÖDINGER TYPE EQUATION

1994 ◽  
Vol 04 (01) ◽  
pp. 49-88 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
MARIE-CLAUDE PELISSIER
Keyword(s):  
Numerical Analysis ◽  
Type Equation ◽  
Neumann Boundary ◽  
Rectangular Domain ◽  
The Other ◽  
Well Posedness ◽  
Discrete Problem ◽  
Spectral Approximation ◽  
Numerical Tests ◽  
Continuous Problem

This paper deals with a linear Schrödinger type equation in a rectangular domain with mixed Dirichlet-Neumann boundary conditions. The well-posedness of the continuous problem is proved, then a discrete problem is defined by combining a Legendre type spectral method in the first direction and a leap-frog scheme in the other one. The numerical analysis of the discretization is performed and error estimates are given. Numerical tests are presented.

scholarly journals Numerical analysis of the characteristics ofCorynebacterium diphtheriaestrains isolated in Victoria from 1962 to 1971

1975 ◽  
Vol 75 (3) ◽  
pp. 413-424
Author(s):  
L. F. Gibson
Keyword(s):  
Numerical Analysis ◽  
Common Ancestor ◽  
Corynebacterium Diphtheriae ◽  
The State ◽  
The Other ◽  
Blood Agar ◽  
Antigenic Structure ◽  
Gradual Change ◽  
Biochemical Activity ◽  
Highly Active

SUMMARYA study of the incidence of diphtheria in the State of Victoria, Australia, was carried out. Numerical analysis of the characteristics of 264 strains ofCorynebacterium diphtheriaeisolated between 1962 and 1971 placed them into 18 varieties plus six strains which were unique in their combination of reactions to the characteristics examined. During the 10-year period, some varieties appeared inter mittently and were recognized by certain defining characteristics but exhibited a gradual change in their antigenic structure. In contrast, when the outbreaks were examined over shorter periods of time, a number of varieties and single strains were found which differed greatly from each other yet possessed the same major serotype antigen. These findings are discussed in terms of a 'one-parent' concept in which the varieties and single strains represent phases of a common ancestor.By inspection and analysis of the characteristics of the strains, certain associations were apparent. For instance, a correlation was found between the antigenic structure of the organism and the colonial appearance on tellurite blood agar. Similarly, correlation was observed between bacteriophage type, diphthericin type and biochemical activity in that a strain which was highly active in one of the properties was also very active in the other two.

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