Nonlinear Inverse Problems in Imaging

Seo, Jin Keun; Woo, Eung Je

doi:10.1002/9781118478141

Cited by 91 publications

(126 citation statements)

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“…The proof is included in the appendix. Note that P (D) in (2.13) is the wave-type differential operator, with x, y as the space and z as the time variable [36], whereas the practical solution χ may not have wave-type structure.…”

Section: Inverse Problemmentioning

confidence: 99%

Inverse Problem in Quantitative Susceptibility Mapping

Choi¹,

Park²,

Wang³

et al. 2014

SIAM J. Imaging Sci.

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Quantitative susceptibility mapping (QSM) is a new medical imaging technique that can visualize magnetic susceptibility, changes of which in tissue indicate various disease processes involving iron transport. The inverse problem of QSM is to recover the susceptibility distribution of the human body from the measured local field that is expressed by the convolution of the susceptibility distribution with the magnetic field generated by a unit dipole. The inverse problem is ill-posed due to the presence of zeros at a cone in the Fourier representation of the unit dipole kernel. Reconstruction methods have been greatly improved to give better recovery of tissue susceptibility data for QSM, and various clinical applications have been pursued. However, rigorous mathematical analyses for the inverse problem, such as demonstrations of the existence and uniqueness of solutions and error characterizations, have not yet been presented. This paper provides for the first time not only a theoretical ground for QSM but also the underlying cause of streaking artifacts.

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Section: Inverse Problemmentioning

confidence: 99%

Inverse Problem in Quantitative Susceptibility Mapping

Choi¹,

Park²,

Wang³

et al. 2014

SIAM J. Imaging Sci.

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“…It uses linearization to construct a sensitivity matrix based on the relation between the boundary potential difference and the conductivity perturbation in the interior of the domain. The ill-posedness of the resulting EIT problem gives low spatial resolution [2,11]. Therefore, we employ an additional imaging technique, called the local projective conductivity image method, using supplementary sensing-only electrodes [12].…”

Section: Local Projective Conductivity Imagementioning

confidence: 99%

Remote Real Time Monitoring for Underground Contamination in Mongolia Using Electrical Impedance Tomography

Lee

Zhou

et al. 2015

J Nondestruct Eval

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Mongolia's abundant natural resources have driven much recent economic development and with it the need for an underground contamination monitoring system. For instance, the fast growth of the mining industry coincides with underground contamination caused by petrol, copper tailings, mercury, etc. These contaminants are highly electrically conductive, and can therefore be assessed by electrical impedance tomography (EIT). This non-destructive and inexpensive method can visualize the conductivity distribution of a target area, and is suited for use in Mongolia. A number of electrodes are placed on the ground surface to induce currents and to measure the resulting voltages. We introduce a new electrode configuration, and use the local projective conductivity image method to monitor the near-surface area. Additionally, conventional EIT is used to monitor areas deeper underground. The collected voltage data can be used for both algorithms-separate measurements are not required-allowing near real-time monitoring for underground contamination. B Eunjung Lee

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“…The Electrical Impedance Tomography (EIT) [11,19,22,33,43,58,78,88,186,209] is computed tomographic technique which provides the 2d or 3D images of the spatial distribution of the electrical properties of a domain under test (Ω) such as electrical conductivity or resistivity from the set of voltage-current data (Fig. 3.11) measured at the domain boundary (∂Ω) surrounded by an array of surface electrodes [29, 140,206].…”

Section: Electrical Impedance Tomography (Eit)mentioning

confidence: 99%