Sensitivity maps in three-dimensional magnetic induction tomography

2012

PIER

Abstract-Magnetic induction tomography (MIT) attempts to image the passive electromagnetic properties (PEP) of an object by measuring the mutual inductances between pairs of coils placed around its periphery. In recent years, there has been an increase in applications of non-contact magnetic induction tomography. When finite element-based reconstruction methods are used, that rely on the inversion of a derivative operator, the large size of the Jacobian matrix poses a challenge since the explicit formulation and storage of the Jacobian matrix could be in general not feasible. This problem is aggravated further in applications for example when the number of coils is increased and in three-dimension. Krylov subspace methods such as conjugate gradient (CG) methods are suitable for such large scale inverse problems. However, these methods require use of the Jacobian matrix, which can be large scale. This paper presents a matrix-free reconstruction method, that addresses the problems of large scale inversion and reduces the computational cost and memory requirements for the reconstruction. The idea behind the matrixfree method is that information about the Jacobian matrix could be available through matrix times vector products so that the creation and storage of big matrices can be avoided. Furthermore the matrix vector multiplications were performed in multiple core fashion so that the computational time can decrease even further. The method was tested for the simulated and experimental data from lab experiments, and substantial benefits in computational times and memory requirements have been observed.

“…Edge FEM in terms of magnetic vector potential (A) is used to simulate the forward eddy current problem [16,17]. Validation of the forward model has been done in a previous study.…”

Section: Forward Problemmentioning

confidence: 99%

“…In [17], the coil geometry needs to be considered when modeling the mesh, which makes the eddy current modeling more difficult and less flexible. In this paper, we define the current source by electric vector potential J s = ∇ × T s .…”

Section: Forward Problemmentioning

confidence: 99%

Three-Dimensional Magnetic Induction Tomography Imaging Using a Matrix Free Krylov Subspace Inversion Algorithm

Wei¹,

2012

PIER

“…In MIT, the forward problems are mainly comprised by the eddy current problems, which are governed by Maxwell's equations [10,11]. The Biot-Savart Law was used in forward model calculations to avoid the coil discretisation in the mesh.…”

Section: Forward Problem -Eddy Current Modelingmentioning

confidence: 99%

“…The sum of the freespace and reduced vector potential A = A s +A e will be used for the sensitivity map calculation, which has been previously derived in [11]. With the (A, A) formulation and the usage of edge finite element, the Sensitivity matrix ( δV δσ ) of the eddy current area can be calculated using dot product of electric fields [11], provided with equations E = −jωA. The sensitivity term between channel i and channel j for conductivity can be expressed as follows:…”

Section: Forward Problem -Eddy Current Modelingmentioning

confidence: 99%

Two-Phase Low Conductivity Flow Imaging Using Magnetic Induction Tomography

Wei¹,

2012

PIER

Abstract-Magnetic Induction Tomography (MIT) is a new and emerging type of tomography technique that is able to map the distribution of all three passive electromagnetic properties, however most of the current interests are focusing on the conductivity and permeability imaging. In an MIT system, coils are used as separate transmitters or sensors, which can generate the background magnetic field and detect the perturbed magnetic field respectively. Through switching technique the same coil can work as transceiver which can generate field at a time and detect the field at another time. Because magnetic field can easily penetrate through the non-conductive barrier, the sensors do not need direct contact with the imaging object. These non-invasive and contactless features make it an attractive technique for many applications compared to the traditional contact electrode based electrical impedance tomography. Recently, MIT has become a promising monitoring technique in industrial process tomography, for example MIT has been used to determine the distribution of liquidised metal and gas (high conductivity two phase flow monitoring) for metal casting applications. In this paper, a low conductivity two phase flow MIT imaging is proposed so the reconstruction of the low contrast samples (< 6 S/m) can be realised, e.g., gas/ionised liquid. An MIT system is developed to test the feasibility. The system utilises 16 coils (8 transmitters and 8 receivers) and an operating frequency of 13 MHz. Three different experiments were conducted to evaluate all possible situations of two phase flow imaging: 1) conducting objects inside a non-conducting background, 2) conducting objects inside a conducting background (low contrast) and 3) non-conducting objects inside a conducting background. Images are reconstructed using the linearised inverse method with regularisation. An experiment was designed to image the non-conductive samples inside a conducting

“…3D MIT is valuable for imaging the volumetric distribution of electrical conductivity and believed to be the future expansion trend of MIT applications. Some of the early work in 3D MIT discuss the sensitivity map calculation and inverse problem [14,15] and has later been validated using a full scaled 3D system [16]. Like other imaging techniques [17][18][19][20][21], 3D MIT systems can only produce sensible results when the measured voltage difference is greater than the system noise level, i.e., adequate signal to noise ratio (SNR).…”

Section: Magnetic Induction Tomography (Mit) Is An Electromagnetic Immentioning

confidence: 99%

Four Dimensional Reconstruction Using Magnetic Induction Tomography: Experimental Study

Wei¹,

2012

PIER

Abstract-Magnetic Induction Tomography (MIT) is a relatively new and emerging type of tomography techniques that is able to map the distribution of all three passive electrical properties (PEPs). Its non-invasive and contactless features make it an attractive technique for many applications compared to the traditional contact electrode based electrical impedance tomography. Recently, MIT has become a promising monitoring technique in industrial process tomography, and the area of the research interest has moved from 2D to 3D because of the volumetric nature of electromagnetic field. Three dimensional MIT images provide more information on the conductivity distribution, especially in the axial direction. However, it has been reported that the reconstructed 3D images can be distorted when the imaging object is located at a less sensitive region. Although this distortion can be compensated by adjusting the regularisation criteria, this is not practical in real life applications as the prior information about the object's location is often unavailable. This paper presents a memory efficient 4D MIT algorithm which can maintain the image quality under the same regularisation circumstances. Instead of solving each set of measurement individually, the 4D algorithm takes advantage of the correlations between the image and its neighboring data frames to reconstruct 4D of conductivity movements. The 4D algorithm improves the image qualities by increasing the temporal resolution. It also overcomes some sensitivity issues of 3D MIT algorithms and can provide a more stable result in terms of the size consistency of the reconstructed image. Several experimental results using real laboratory data are presented for validating the proposed algorithms.