Effects of simulated error-sources on different 3-D CSI-EPT strategies

Three-dimensional contrast source inversion-electrical properties tomography (3-D CSI-EPT) is an iterative reconstruction method that estimates the electrical properties of tissue from transmit field magnetic resonance data. However, in order to bring 3-D CSI-EPT into practice for complex tissue structures and to understand the origin and effect of errors, insight in the sensitivities of reconstruction accuracy to the major error-sources is necessary. In this paper, different strategies for implementing 3-D CSI-EPT, including their iterative structure, are presented, of which the regularized implementation shows the most potential to be used in practice. Moreover, the influence of initialization, noise, stopping criteria, incident fields, B1-maps, transceive phase and domain truncation are discussed. We show that of all these different error-sources, initialization, accurate coil models and domain truncation have the most dramatic effect on electrical properties reconstructions in practice.Imaging- and therapeutic targets in neoplastic and musculoskeletal inflammatory diseas

On Algorithms Based on Joint Estimation of Currents and Contrast in Microwave Tomography

This paper deals with improvements to the contrast source inversion method which is widely used in microwave tomography. First, the method is reviewed and weaknesses of both the criterion form and the optimization strategy are underlined. Then, two new algorithms are proposed. Both of them are based on the same criterion, similar but more robust than the one used in contrast source inversion. The first technique keeps the main characteristics of the contrast source inversion optimization scheme but is based on a better exploitation of the conjugate gradient algorithm. The second technique is based on a preconditioned conjugate gradient algorithm and performs simultaneous updates of sets of unknowns that are normally processed sequentially. Both techniques are shown to be more efficient than original contrast source inversion.Comment: 12 pages, 12 figures, 5 table

Imaging of a fluid injection process using geophysical data - A didactic example

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts

Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography

Heat as a proxy to image dynamic processes with 4D electrical resistivity tomography

Since salt cannot always be used as a geophysical tracer (because it may pollute the aquifer with the mass that is necessary to induce a geophysical contrast), and since in many contaminated aquifer salts (e.g., chloride) already constitute the main contaminants, another geophysical tracer is needed to force a contrast in the subsurface that can be detected from surface geophysical measurements. In this context, we used heat as a proxy to image and monitor groundwater flow and solute transport in a shallow alluvial aquifer (< 10 m deep) with the help of electrical resistivity tomography (ERT). The goal of our study is to demonstrate the feasibility of such methodology in the context of the validation of the efficiency of a hydraulic barrier that confines a chloride contamination to its source. To do so, we combined a heat tracer push/pull test with time-lapse 3D ERT and classical hydrogeological measurements in wells and piezometers. Our results show that heat can be an excellent salt substitution tracer for geophysical monitoring studies, both qualitatively and semi-quantitatively. Our methodology, based on 3D surface ERT, allows to visually prove that a hydraulic barrier works efficiently and could be used as an assessment of such installations

Pavement testing by integrated geophysical methods: Feasibility, resolution and diagnostic potential

This work is focused on the assessment of the diagnostic potential of several geophysical methods when applied to the investigation of a rigid airport pavement. The potential and limit of each technique are evaluated as well as the added value deriving from their integration. Firstly, we reconstruct a high-resolution image of the pavement by a large electromagnetic and georadar screening. An advanced processing of georadar data, implemented through the picking of the arrival times of reflections for each profile, provides a quantitative estimation of the deviation between the design and the as-built thickness of layers. Additionally, electrical tomography has been applied to unequivocally identify the anomalous zones, where higher values of resistivity would be associated to porous zones that are prone to degradation and failure. The seismic tomographic survey had the additional purpose to recover the mechanical properties of the pavement in terms of both P- and S-waves and consequently of elastic constants (Poisson's ratio), whose values were consistent with those recovered in literature. The anomalies detected by each technique are consistent in their indications and they can be correlated to failure phenomena occurring at layer interfaces within the pavement structure or to unexpected variations of the layer thicknesses. The cost-effective geophysical campaign has validated the four-layered system deduced from the original design and has been used to reconstruct a high-resolution map of the pavement in order to discriminate fractures, crack-prone areas or areas where the as-built differs from the original design

A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable Electrical Impedance Tomography. In the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with MAET. It consists in applying to the data one of the algorithms of Thermo-Acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data