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### Page 3937 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews
Interesting and useful solutions to many phase unwrapping problems can be obtained when p < 2.  ...  /’-norm two-dimensional phase unwrapping.  ...

### Isotropic inverse-problem approach for two-dimensional phase unwrapping

Ulugbek S. Kamilov, Ioannis N. Papadopoulos, Morteza H. Shoreh, Demetri Psaltis, Michael Unser
2015 Optical Society of America. Journal A: Optics, Image Science, and Vision
In this paper, we propose a new technique for two-dimensional phase unwrapping.  ...  The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional.  ...  If, for a given pixel n ∈ [1, . . . , N], the unwrapped phase φ satisfies [Dφ] n 2 ([D x φ] n ) 2 + ([D y φ] n ) 2 ≤ π, (3) then, we have the equality [Dφ] n = W ([Dψ] n ). (4) Here, [Dφ] n ([D x φ] n  ...

### Isotropic inverse-problem approach for two-dimensional phase unwrapping [article]

Ulugbek S. Kamilov, Ioannis N. Papadopoulos, Morteza H. Shoreh, Demetri Psaltis, Michael Unser
2015 arXiv   pre-print
In this paper, we propose a new technique for two-dimensional phase unwrapping.  ...  The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional.  ...  If, for a given pixel n ∈ [1, . . . , N ], the unwrapped phase φ satisfies [Dφ] n 2 ([D x φ] n ) 2 + ([D y φ] n ) 2 ≤ π, (3) then, we have the equality [Dφ] n = W([Dψ] n ). (4) Here, [Dφ] n ([D x φ] n  ...

### Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging [article]

Fangshu Yang, Thanh-an Pham, Nathalie Brandenberg, Matthias P. Lutolf, Jianwei Ma, Michael Unser
2020 arXiv   pre-print
Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the computational process that recovers a more informative image.  ...  Our framework relies on an untrained convolutional neural network to accurately unwrap the phase while ensuring the consistency of the measurements.  ...  Generally, the path-following methods encounter issues of consistency as the resulting unwrapped phase depends on the path. By contrast, the minimum-norm methods are global.  ...

### Fast InSAR multichannel phase unwrapping for DEM generation

Giampaolo Ferraioli, Aymen Shabou, Florence Tupin, Vito Pascazio
2009 2009 Joint Urban Remote Sensing Event
In this paper, a method to solve the multichannel phase unwrapping problem is presented.  ...  The idea is to develop a fast algorithm to unwrap the interferometric phase in the multichannel configuration, which is, in the main time, able to provide the global optimum solution.  ...  Even the method proposed by Bioucas  , based on a L p norm phase unwrapping method using graph-cuts, is not able to properly unwrap the considered interferogram.  ...

### Reconstruction of aerial images from uniformly sampled magnitude Fourier spectra using spectral statistical models

Oliver M. Jeromin, Marios S. Pattichis
2009 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers
We approach this problem by exploring the magnitude and phase spectra independently.  ...  The reconstructed spectral components are compared to other widely used 2D interpolation algorithms (cubic splines, nearest neighbor, and bilinear interpolators).  ...  The 2-D phase unwrapping techniques are the three path following techniques: Goldstein's Branch Cut method, quality guided path following, and Flynn's minimum discontinuity method.  ...

### Multiscale Sampling Geometries and Methods for Deterministic and Stochastic Reconstructions of Magnitude and Phase Spectra of Satellite Imagery

Oliver Jeromin, Marios S. Pattichis
2012 IEEE Transactions on Geoscience and Remote Sensing
To develop effective models, the magnitude spectrum is preprocessed using a logarithmic transformation. Phase interpolation requires preprocessing by an appropriate phase unwrapping method.  ...  The results indicate that the stochastic (Kriging) interpolation approach provides the best rural image reconstructions using just 6.01% of the 2-D FFT samples.  ...  The other two methods can be described as minimum norm methods, which approach phase unwrapping in a mathematically formal manner.  ...

### Phase Unwrapping for 2-D Blind Deconvolution of Ultrasound Images

2004 IEEE Transactions on Medical Imaging
The present study demonstrates a principally novel approach to the problem of phase unwrapping, which commonly arises as a part of the 2-D homomorphic deconvolution of ultrasound images.  ...  The proposed method is compared with the classical approaches, which use estimates of the discrete partial derivatives of unwrapped FT-phases of RF-images.  ...  C D = = Β Β − + Β Β − D D F F 2 (4.5) Here denotes the Frobeniuos matrix norm.  ...

### A family of approximations spanning the Born and Rytov scattering series

Daniel L. Marks
2006 Optics Express
Also included is the integral equation that defines the exact solution to the forward scattering problem as well as its Fréchet derivative, which is used for the solution of inverse multiple scattering  ...  Minimizing L finds the minimum-norm solution to Eq. ( 9 ) for φ and κ.  ...  To implement the inverse, the complex phase {φ } is calculated from the measured fields {u} using Eq. ( 27 ) including phase unwrapping.  ...

### Coseismic and postseismic deformation estimation of the 2011 Tohoku earthquake in Kanto Region, Japan, using InSAR time series analysis and GPS

Tamer ElGharbawi, Masayuki Tamura
2015 Remote Sensing of Environment
In that 421 case, the SVD can be used to invert the system, but that can produce unrealistic deformation 422 values because the SVD adopts the minimum norm solution.  ...  348 phase maps(Fig. 3, Step D).  ...

### Quantitative phase imaging of biological cells using spatially low and temporally high coherent light source

Azeem Ahmad, Vishesh Dubey, Gyanendra Singh, Veena Singh, Dalip Singh Mehta
2016 Optics Letters
Moreover, some of the DIC techniques can also provide the quantitative information about the biological specimens    .  ...  In this Letter, we demonstrate quantitative phase imaging of biological samples, such as human red blood cells (RBCs) and onion cells using narrow temporal frequency and wide angular frequency spectrum  ...  The minimum L P -norm two-dimensional phase unwrapping algorithm Fig. 4(d) , there are a few artifacts present in the background of the RBCs phase image.  ...

### Bayesian neural-networks-based evaluation of binary speckle data

Udo V. Toussaint, Silvio Gori, Volker Dose
2004 Applied Optics
We present a new method using Bayesian probability theory and neural networks for the evaluation of speckle interference patterns for an automated analysis of deformation and erosion measurements.  ...  Given a binary speckle image, the method returns the fringe pattern without noise, thus removing the need for smoothing and allowing a straight-forward unwrapping procedure and determination of the surface  ...  For comparison the result of a wavelet analysis 26 is given in Fig. 4a . subsequently into height fields through a straightforward post-processing stage using phase unwrapping techniques (e.g. 26, 29  ...

### Asymptotic behavior of future-complete cosmological space-times [article]

Michael T. Anderson
2004 arXiv   pre-print
Evaluating (7.5) at a point realizing the minimum of φ then gives (7.6)R ≥ − 2 3 τ 2 , i.e. the Yamabe metricĝ has scalar curvature ≥ − 2 3 τ 2 .  ...  Thus, the CMC foliation F gives a 3 + 1 decomposition of (M, g) as (6.7) g = −α 2 dτ 2 + g τ = −α 2 ( dτ dt τ ) 2 dt 2 τ + g τ .  ...

### Multi-Incidence Holographic Profilometry for Large Gradient Surfaces with Sub-Micron Focusing Accuracy

Moncy Sajeev Idicula, Tomasz Kozacki, Michal Józwik, Patryk Mitura, Juan Martinez-Carranza, Hyon-Gon Choo
2021 Sensors
Surface reconstruction for micro-samples with large discontinuities using digital holography is a challenge.  ...  Other phase-based autofocusing algorithms were tested as well. The NORM L1  and VAR  algorithms were used to calculate the focus plane.  ...  The NORM L1  and VAR  algorithms were used to calculate the focus plane.  ...

### Phase Estimation for Distributed Scatterers in InSAR Stacks Using Integer Least Squares Estimation

Sami Samiei-Esfahany, Joana Esteves Martins, Freek van Leijen, Ramon F. Hanssen
2016 IEEE Transactions on Geoscience and Remote Sensing
We model the SM-phase estimation problem in a linear form by introducing additional integer ambiguities and use a bootstrap estimator for joint estimation of SM-phases and the integer unknowns.  ...  The key step in these algorithms is to optimally estimate single-master (SM) wrapped phases for each pixel from all possible interferometric combinations, preserving useful information and filtering noise  ...  ) 3 D 1 2 exp − 1 2 y T slc k D −1 y slc k . (22) D is a 2N × 2N covariance matrix given by (assuming zeromean phase) D = C 0 0 C (23) where C is the N × N absolute coherence matrix of y slc k .  ...
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