Phase Unwrapping

Ying, Leslie

doi:10.1002/9780471740360.ebs1356

Cited by 40 publications

(31 citation statements)

References 32 publications

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“…The output EM data include the amplitude and the phase of the axial component, which need to be processed before being imaged with the simultaneous iterative reconstruction technique (SIRT) algorithm. The processes that we use to manipulate the amplitude data are known as amplitude data reduction (Jackson and Tweeton 1994); the phase data processing is known as phase recovery (Ying 2006).…”

Section: E T H O D O L O G Ymentioning

confidence: 99%

Modelling and straight‐ray tomographic imaging studies of cross‐hole radio‐frequency electromagnetic data for mineral exploration

Smith

2017

Geophysical Prospecting

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Radio‐frequency electromagnetic tomography (or radio imaging method) employs radio‐frequency (typically 0.1–10 MHz) electromagnetic wave propagation to delineate the distribution of electric properties between two boreholes. Currently, the straight‐ray imaging method is the primary imaging method for the radio imaging method data acquired for mineral exploration. We carried out synthetic studies using three‐dimensional finite‐element modelling implemented in COMSOL Multiphysics to study the electromagnetic field characteristics and to assess the capability of the straight‐ray imaging method using amplitude and phase data separately. We studied four sets of experiments with models of interest in the mining setting. In the first two experiments, we studied models with perfect conductors in homogeneous backgrounds, which show that the characteristics of the electromagnetic fields depend mainly on the wavelength. When the borehole separations are less than one wavelength, induction effects occur; conductors with simple geometries can be recovered acceptably with amplitude data but are incorrectly imaged on the phase tomogram. When the borehole separations are longer than two wavelengths, radiation effects play a major role. In this case, phase tomography provides images with acceptable quality, whereas amplitude tomography does not provide satisfactory results. The third experiment shows that imaging with both original and reciprocal datasets is somewhat helpful in improving the imaging quality by reducing the impact of noise. In the last experiment, we studied models with conductive zones extended into the borehole plane with different lengths, which were not accurately recovered with amplitude tomography. The experiment implies that it is difficult to determine the extent of a mineralised zone that has been intersected by one of the boreholes. Due to the large variation of the wavelength in the radio‐frequency range, we suggest investigating the local electric properties to select an operating frequency prior to a survey. We conclude that straight‐ray tomography with either amplitude or phase data cannot provide high‐quality imaging results. We suggest using more general methods based on full electromagnetic modelling to interpret the data. In circumstances when computational time is critical, we suggest saving time by using either induction methods for borehole separations less than one wavelength or wave‐based methods (only radiation fields are considered) for borehole separation larger than two wavelengths.

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Section: E T H O D O L O G Ymentioning

confidence: 99%

Modelling and straight‐ray tomographic imaging studies of cross‐hole radio‐frequency electromagnetic data for mineral exploration

Smith

2017

Geophysical Prospecting

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“…Interestingly, if the Itoh smoothness condition is satisfied and there is no noise in the measurement (n = 0), the image gradient can be indirectly observed through the following relation [3,9]:…”

Section: Discrete Forward Modelmentioning

confidence: 99%

Robust phase unwrapping by convex optimization

Gonzalez

Jacques

2014

2014 IEEE International Conference on Image Processing (ICIP)

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The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo 2π observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by recording complex or modulated data from which a "wrapped" phase is extracted. Although 1-D phase unwrapping is trivial, a challenge remains in higher dimensions to overcome two common problems: noise and discontinuities in the true phase image. In contrast to state-of-the-art techniques, this work aims at simultaneously unwrap and denoise the phase image. We propose a robust convex optimization approach that enforces data fidelity constraints expressed in the corrupted phase derivative domain while promoting a sparse phase prior. The resulting optimization problem is solved by the Chambolle-Pock primal-dual scheme. We show that under different observation noise levels, our approach compares favorably to those that perform the unwrapping and denoising in two separate steps.

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“…Two-dimensional unwrapping algorithms exist 23 that would allow the unwrapping of the matrix U across microphone pairs without broadband information, but this approach would be useful only for a one-dimensional array and is limited in how far above the spatial Nyquist frequency meaningful results are produced. 25 Once the phase is unwrapped, UPAINT interpolates M Â M matricesŨ and jCj to M 0 Â M 0 matricesŨ 0 and jC 0 j using bilinear interpolation, where M 0 is the total number of array elements after interpolation. These interpolated matrices become the phase and magnitude of the virtual cross spectral matrix C 0 .…”

Section: The Upaint Methodsmentioning

confidence: 99%

Extending the bandwidth of an acoustic beamforming array using phase unwrapping and array interpolation

Goates

Harker

Neilsen

et al. 2017

The Journal of the Acoustical Society of America

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A method is presented to suppress grating lobes in beamforming using phase unwrapping and array interpolation. When the phase of each cross spectrum is successfully unwrapped, the magnitude and phase of the cross spectral matrix may be interpolated; for cases where these quantities vary smoothly, interpolation is straightforward, even above the spatial Nyquist frequency. Two applications are presented: localization of a broadband source and characterization of a source with frequency-dependent location. In both cases, grating lobes are suppressed and the source is localized at frequencies up to at least 8 times the spatial Nyquist frequency.

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Phase Unwrapping

Cited by 40 publications

References 32 publications

Modelling and straight‐ray tomographic imaging studies of cross‐hole radio‐frequency electromagnetic data for mineral exploration

Modelling and straight‐ray tomographic imaging studies of cross‐hole radio‐frequency electromagnetic data for mineral exploration

Robust phase unwrapping by convex optimization

Extending the bandwidth of an acoustic beamforming array using phase unwrapping and array interpolation

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