Search results for "Phase problem"

showing 6 items of 6 documents

Optical phase retrieval using four rotated versions of a single binary mask – simulation results

2018

In signal processing one often faces the phase problem, i.e., when an image is formed information about the phase is lost so that only information about intensity is available. This is often an issue in astronomy, biology, crystallography, speckle imaging, diffractive imaging where the phase of the object must be known. While there have been many approaches how to find a solution to the phase problem, numerical algorithms recovering the phase from intensity measurements become more and more popular. One of such algorithms called PhaseLift has been recently proposed. In this study, we show that even 4 masks may be sufficient for reasonable recovery of the phase. The original wavefront and th…

WavefrontSignal processingComputer scienceFourier opticsPhase (waves)010103 numerical & computational mathematicsPhase problem01 natural sciences010309 optics0103 physical sciencesSpeckle imaging0101 mathematicsPhase retrievalAdaptive opticsAlgorithmComputational Optics II
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The Effect of the Range of a Modulating Phase Mask on the Retrieval of a Complex Object from Intensity Measurements

2021

The authors have been supported by the postdoctoral project (1.1.1.2/16/I/001, 1.1.1.2/VIAA/1/16/199), the CAMART2 project (grant agreement ID 739508), the Latvian Investment and Development Agency (LIDA) project (KC-PI-2017/105), and the grant for the Latvian State Emeritus Scientists.

phase retrievalComputer Science::Information RetrievalPhysicsQC1-999phase problem020206 networking & telecommunications02 engineering and technology01 natural sciences010309 opticscoherent diffractive imaging0103 physical sciences0202 electrical engineering electronic engineering information engineering:NATURAL SCIENCES [Research Subject Categories]Coherent diffractive imagingmagnitude
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Positive solutions for singular (p, 2)-equations

2019

We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.

Dirichlet problemApplied MathematicsGeneral Mathematics010102 general mathematicsNonparametric statisticsSingular termGeneral Physics and AstronomyPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi MatematicaSingular term Superlinear perturbation Positive solution Nonlinear regularity Truncation Maximum principle Double phase problemApplied mathematics0101 mathematicsLaplace operatorMathematicsZeitschrift für angewandte Mathematik und Physik
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Positive solutions for singular double phase problems

2021

Abstract We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a p-Laplacian and of a weighted q-Laplacian ( q p ) with discontinuous weight. Using the Nehari method, we show that for all small values of the parameter λ > 0 , the equation has at least two positive solutions.

Class (set theory)Double phase problemNehari manifold01 natural sciencesDirichlet distributionsymbols.namesakeMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: MathematicsApplied mathematics0101 mathematics35J60 35D05Positive solutionsParametric statisticsMathematicsApplied Mathematics010102 general mathematicsSingular termSingular termMathematics::Spectral TheoryDifferential operatorTerm (time)010101 applied mathematicsDouble phaseDiscontinuous weightsymbolsAnalysisAnalysis of PDEs (math.AP)
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The effect of noise, a constant background, and bit depth on the phase retrieval of pure phase objects

2021

Acknowledgements – The authors are supported by the postdoctoral project (1.1.1.2/16/I/001; 1.1.1.2/ VIAA/1/16/199, State Education Development Agency, Republic of Latvia).

phase retrievalNoiseComputer scienceAcousticsphase problemColor depthPhase (waves)diffraction:NATURAL SCIENCES::Physics [Research Subject Categories]Constant (mathematics)Phase retrievalAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic Materials
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A two-phase problem with Robin conditions on the free boundary

2020

We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers. peerReviewed

Class (set theory)General MathematicsBoundary (topology)variaatiolaskentaRobin boundary conditionsPhase problemRobin boundary condition01 natural sciencesFree boundary problemsRegularityMathematics - Analysis of PDEsFOS: MathematicsFree boundary problemApplied mathematics0101 mathematicsMathematicsosittaisdifferentiaaliyhtälöt010102 general mathematicsFree boundary problemFree boundary problems; Regularity; Robin boundary conditions; Two-phasematemaattinen optimointi16. Peace & justiceRobin boundary condition010101 applied mathematicsTwo-phaseAnalysis of PDEs (math.AP)
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