Propagation of measurement noise through backprojection reconstruction in electrical impedance tomography

Frangi, Alejandro F.; Riu, Pere J.; Rosell, J.; Viergever, Max A.

doi:10.1109/tmi.2002.800612

Cited by 20 publications

(15 citation statements)

References 50 publications

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“…This effect is further noticeable for reconstruction from noisy data, where the algorithm reconstructs only first three layers, and can not "penetrate" beyond it. The input data bases include both noiseless data sets and noisy sets [19] characterized by 60 dB signal to noise ratio (SNR), with respect to the signal V (sρ) at the endpoint of Legendre window w = 1 (11) and a specified scaling factor s = 1. SNR level of 60 dB can be experimentally maintained utilizing the readily available narrow-band lowfrequency active filters.…”

Section: Results -Reconstruction Examplementioning

confidence: 99%

Electrical Impedance Tomography Method for Reconstruction of Biological Tissues with Continuous Plane-Stratification

Dolgin

Einziger

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

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A novel electrical impedance tomography method is introduced for reconstruction of layered biological tissues with continuous plane-stratification. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, based on an improved Prony method in conjunction with Legendre polynomial expansion (LPE). It is shown that the proposed algorithm is capable of successfully reconstructing continuous conductivity profiles with moderate (WKB) slop. Features of the presented reconstruction scheme include, an inherent linearity, achieved by the linear LPE transform, a locality feature, assigning analytically to each spectral component a local electrical impedance associated with a unique location, and effective performance even in the presence of noisy measurements.

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Section: Results -Reconstruction Examplementioning

confidence: 99%

Electrical Impedance Tomography Method for Reconstruction of Biological Tissues with Continuous Plane-Stratification

Dolgin

Einziger

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

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“…Considering the fact that the discretized gradient descent speed v gd is equal to J T (u − z) [60], both Gauss-Newton-type and projection-based speed vectors can also be considered as scaled versions of v gd . According to (30), v GN can be expressed as…”

Section: Projection-based Approach and The Gauss-newton Methodmentioning

confidence: 99%

“…In the literature, several iterative and noniterative reconstruction methods have been proposed for addressing the conductivity reconstruction problem (see the topical reviews [25][26][27]). Noniterative techniques include the backprojection algorithm [28][29][30], layer stripping methods [33][34][35] and the ∂ method [36,37]. Another method is the NOSER algorithm [9,31,32] which is a single Gauss-Newton step regularized with a diagonal approximation of the Hessian.…”

Section: Introductionmentioning

confidence: 99%

A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography

Miled

Miller

2007

Inverse Problems

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In this paper we consider level-set-based methods for anomaly reconstruction for applications involving low-sensitivity data concentrating specifically on the problem of electrical resistance tomography (ERT). Typical descent-based inversion methods suffer from poor reconstruction precision in low-sensitivity regions and typically display quite slow convergence. In this paper, we develop a method for constructing the level-set speed function that is capable of overcoming these problems. In the case of the gradient-descent-based level-set evolution, the speed function is defined in terms of the dot products of residual and sensitivity functions. For Gauss-Newton-type methods, however, the speed function is the solution of the linearized inverse problem at each iteration. Here we propose a projection-based approach where the displacement of the level zero, i.e. estimated anomaly contour, at each point depends on the correlation coefficients between the sensitivity of the data to conductivity perturbations and the residual error. In other words, the proposed velocity field is invariant to the absolute amplitudes of both residual and sensitivity, but rather is a reflection of the angle between these two quantities. We demonstrate that our method is a descent-based reconstruction and we relate the mathematical formulation of the projection-based speed function to that of the gradient-descent method and the Gauss-Newton-type approach. The comparison suggests that the proposed technique can be seen as a diagonal approximation of the Gauss-Newton formulation. Using a quasi-linear source-type formulation of the forward problem, we describe an efficient implementation of the projectionbased approach for finite-domain imaging problems. The proposed algorithm is simulated with numerical 2D and 3D data and its performance and efficiency are compared to those of the gradient-descent method.

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“…In addition the noise of the excitation coils is propagated to all receiver coils, thus resulting in a certain amount of correlated noise in all receiver channels. This phenomenon has been studied in detail for EIT,6 but should be disregarded here for simplicity.…”

Section: Methodsmentioning

confidence: 99%

Single-Step 3-D Image Reconstruction in Magnetic Induction Tomography: Theoretical Limits of Spatial Resolution and Contrast to Noise Ratio

et al. 2006

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Abstract-Magnetic induction tomography (MIT) is a lowresolution imaging modality for reconstructing the changes of the complex conductivity in an object. MIT is based on determining the perturbation of an alternating magnetic field, which is coupled from several excitation coils to the object. The conductivity distribution is reconstructed from the corresponding voltage changes induced in several receiver coils. Potential medical applications comprise the continuous, non-invasive monitoring of tissue alterations which are reflected in the change of the conductivity, e.g. edema, ventilation disorders, wound healing and ischemic processes. MIT requires the solution of an ill-posed inverse eddy current problem. A linearized version of this problem was solved for 16 excitation coils and 32 receiver coils with a model of two spherical perturbations within a cylindrical phantom. The method was tested with simulated measurement data. Images were reconstructed with a regularized single-step GaussNewton approach. Theoretical limits for spatial resolution and contrast/noise ratio were calculated and compared with the empirical results from a Monte-Carlo study. The conductivity perturbations inside a homogeneous cylinder were localized for a SNR between 44 and 64 dB. The results prove the feasibility of difference imaging with MIT and give some quantitative data on the limitations of the method.

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Propagation of measurement noise through backprojection reconstruction in electrical impedance tomography

Cited by 20 publications

References 50 publications

Electrical Impedance Tomography Method for Reconstruction of Biological Tissues with Continuous Plane-Stratification

Electrical Impedance Tomography Method for Reconstruction of Biological Tissues with Continuous Plane-Stratification

A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography

Single-Step 3-D Image Reconstruction in Magnetic Induction Tomography: Theoretical Limits of Spatial Resolution and Contrast to Noise Ratio

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