Conditional Bayes reconstruction for ERT data using resistance monotonicity information

Abstract

Abstract. Many applications of tomography seek to image two-phase materials, such as oil and air, with the idealized aim of producing a binary reconstruction. The method of Tamburrino et al. (2002) provides a non-iterative approach, which requires modest computational effort, and hence appears to achieve this aim. Specifically, it requires the solution of a number of forward problems increasing only linearly with the number of elements used to represent the domain where the resistivity is unknown. However, even when low measurement noise is present it may be that not all domain elements can be classified and hence only a partial reconstruction is possible. This paper looks at the use of a Bayesian approach based on the monotonicity information for reconstructing the shape of a homogeneous resistivity inclusion in another homogeneous resistivity material. In particular, the monotonicity criterion is used to fix the resistivity of some pixels. The uncertain pixel resistivities are then estimated, conditional upon the fixed values. This has the effect of both producing better reconstructions, but also reducing the computational burden by up to an order of magnitude in the examples considered. The methods are illustrated using simulation examples covering a range of object geometries.

Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography

“…After scaling, the reference conductivity is σ 0 = 1 S/m, and D still denotes the Plexiglas rod with conductivity σ = 0 S/m. Thus, γ = 1, a − = inf D γ = 1 and β k is calculated using (4). In practice, there is no way to obtain the exact value of the matrix V in (4).…”

“…Thus, γ = 1, a − = inf D γ = 1 and β k is calculated using (4). In practice, there is no way to obtain the exact value of the matrix V in (4). Indeed, what we know is just the measured data V δ = U δ (σ) − U δ (σ 0 ), where δ denotes the noise level.…”

“…It is worth to mention that our new algorithm is non-iterative, hence, it does not depend on an initial guess and does not require expensive computation. Other non-iterative algorithms, for example, the Factorization Method [15,16] and the Monotonicity-based Method [31,30,22,4], on the other hand, are much more sensitive to measurement errors than our new algorithm when phantom data or real data are applied [5,21,33,10].…”

Appraisal of Resistivity Inversion Models With Convolutional Variational Encoder–Decoder Network

“…After extracting the structural orientation from geological sections, Zhou et al [13] used a model covariance matrix in order to improve the inversion findings. Robert G Aykroyd et al [14] proposed a Bayesian approach to reconstruct the shape of a homogeneous resistivity based on monotonicity information.…”

Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography

“…Such iterative methods yield good reconstructions for a given good initial guess; however, they require expensive computation and have no convergence results. Non-iterative methods such as the Factorization Method ( [17,18]) and the Monotonicity-based Method ( [35,34,22,3]), on the other hand, are rigorously justified and require no initial guess. However, the reconstructions of both Factorization Method and Monotonicity-based Method tend to be rather sensitive to measurement errors when phantom data or real data are applied [4,21,39,11].…”