Enforcing a minimum-phase condition on an arbitrary one-dimensional signal with application to a two-dimensional phase retrieval problem

2002 ◽  
Author(s):  
Wooshik Kim
Keyword(s):  
Phase Retrieval ◽  
Minimum Phase ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Condition ◽  
Retrieval Problem

Uniqueness of a one-dimensional phase retrieval problem

2014 ◽  
Vol 30 (7) ◽  
pp. 075004 ◽  
Author(s):  
Michael V Klibanov ◽  
Vladimir G Kamburg
Keyword(s):  
Phase Retrieval ◽  
One Dimensional ◽  
Retrieval Problem

scholarly journals The New TLC Method for Separation and Determination of Multicomponent Mixtures of Plant Extracts

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Elżbieta Matysik ◽  
Anna Woźniak ◽  
Roman Paduch ◽  
Robert Rejdak ◽  
Beata Polak ◽  
...  
Keyword(s):  
Thin Layer ◽  
Thin Layer Chromatography ◽  
Gradient System ◽  
Two Dimensional ◽  
Phase Gradient ◽  
One Dimensional ◽  
Dominant Component ◽  
Phase Condition ◽  
Layer Chromatography

The new mode of two-dimensional gradient thin layer chromatography (MGD-2D TLC) has been presented. Short distance development of sample in the first dimension leads to formation of the preconcentrated narrow zones. They are consecutively separated in the second dimension with the mobile phase gradient in several steps of development until the eluent reaches the further end of the chromatographic plate. The use of the above-mentioned technique allows isolating and then identifying the compounds of various polarity from the multicomponent mixture. The practical application of two-dimensional gradient thin layer chromatography has been performed for isolation of the two plant (JuniperusandThymus) oils components as the examples of test mixtures. The experiments have been carried out with the use of silica gel plates as well as a normal phase condition. The results of solute separation with isocratic one-dimensional thin layer chromatography system have been compared with those of two-dimensional gradient system. It has been observed that application of the latter mode leads to almost triplicated number of zones in comparison with the former one. It is purposeful to apply the proposed mode to control the purity of the dominant component or components of the mixture.

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

On Two-Dimensional Hilbert Integral Equations, Generalized Minimum-Phase Signals, and Phase Retrieval

2018 ◽  
Vol 66 (14) ◽  
pp. 3906-3917 ◽  
Author(s):  
Basty Ajay Shenoy ◽  
Satish Mulleti ◽  
Chandra Sekhar Seelamantula
Keyword(s):  
Integral Equations ◽  
Phase Retrieval ◽  
Minimum Phase ◽  
Two Dimensional ◽  
Hilbert Integral

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

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