Lauri Harhanen

Edge-enhancing reconstruction algorithm for three-dimensional electrical impedance tomography

Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori known that the conductivity consists of embedded inhomogeneities in an approximately constant background. This work introduces an iterative reconstruction algorithm that aims at finding the maximum a posteriori estimate for the conductivity assuming an edge-preferring prior. The method is based on applying (a single step of) priorconditioned lagged diffusivity iteration to sequential linearizations of the forward model. The algorithm is capable of producing reconstructions on dense unstructured three-dimensional finite element meshes and with a high number of measurement electrodes. The functionality of the proposed technique is demonstrated with both simulated and experimental data in the framework of the complete electrode model, which is the most accurate model for pract...

Sweep data of electrical impedance tomography

This work considers electrical impedance tomography in the special case that the boundary measurements of current and voltage are carried out with two (infinitely) small electrodes. One of the electrodes lies at a fixed position while the other is moved along the object boundary in a sweeping motion, with the corresponding measurement being the (relative) potential difference required for maintaining a unit current between the two electrodes. Assuming that the two-dimensional object of interest has constant background conductivity but is contaminated by compactly supported inhomogeneities, it is shown that such sweep data represent the boundary value of a holomorphic function defined in the exterior of the embedded inclusions. This observation makes it possible to use the sweep data as the input for the convex source support method in order to localize conductivity inhomogeneities. The functionality of the resulting algorithm is demonstrated by numerical experiments both with idealized point electrode data and with simulated complete electrode model measurements.

Iterated preconditioned LSQR method for inverse problems on unstructured grids

This article presents a method for solving large-scale linear inverse imaging problems regularized with a nonlinear, edge-preserving penalty term such as total variation or the Perona–Malik technique. Our method is aimed at problems defined on unstructured meshes, where such regularizers naturally arise in unfactorized form as a stiffness matrix of an anisotropic diffusion operator and factorization is prohibitively expensive. In the proposed scheme, the nonlinearity is handled with lagged diffusivity fixed point iteration, which involves solving a large-scale linear least squares problem in each iteration. Because the convergence of Krylov methods for problems with discontinuities is notoriously slow, we propose to accelerate it by means of priorconditioning (Bayesian preconditioning). priorconditioning is a technique that, through transformation to the standard form, embeds the information contained in the prior (Bayesian interpretation of a regularizer) directly into the forward operator and thence into the solution space. We derive a factorization-free preconditioned LSQR algorithm (MLSQR), allowing implicit application of the preconditioner through efficient schemes such as multigrid. The resulting method is also matrix-free i.e. the forward map can be defined through its action on a vector. We illustrate the performance of the method on two numerical examples. Simple 1D-deblurring problem serves to visualize the discussion throughout the paper. The effectiveness of the proposed numerical scheme is demonstrated on a three-dimensional problem in fluorescence diffuse optical tomography with total variation regularization derived algebraic multigrid preconditioner, which is the type of large scale, unstructured mesh problem, requiring matrix-free and factorization-free approaches that motivated the work here.

Dynamic multi-source X-ray tomography using a spacetime level set method

A novel variant of the level set method is introduced for dynamic X-ray tomography. The target is allowed to change in time while being imaged by one or several source-detector pairs at a relatively high frame-rate. The algorithmic approach is motivated by the results in 22], showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography. Furthermore, defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here. The tomographic reconstruction is found as a minimizer of a nonlinear functional. The functional contains a regularization term penalizing the L 2 norms of up to n derivatives of the reconstruction. The case n = 1 is shown to be equivalent to a convex Tikhonov problem that has a unique minimizer. For n ? 2 the existence of a minimizer is proved under certain assumptions on the signal-to-noise ratio and the size of the regularization parameter. Numerical examples with both simulated and measured dynamic X-ray data are included, and the proposed method is found to yield reconstructions superior to standard methods such as FBP or non-negativity constrained Tikhonov regularization and favorably comparable to those of total variation regularization. Furthermore, the methodology can be adapted to a wide range of measurement arrangements with one or more X-ray sources.

Damage detection in CFRP components using DIC

Unidirectional carbon fiber reinforced polymer composites (UD CFRP) are high performance materials for structural components, but they are very sensitive to damage. Structural health monitoring is therefore required in safety-critical applications. Many non-destructive evaluation techniques are not suitable for in-service monitoring, which calls for new approaches. We investigate the use of full-field digital image correlation (DIC) for detecting damage in UD CFRP components. Stereo-DIC data is used to analyze changes in vibration modes due to artificial defects. Finally, the effect of the defects is assessed and the suitability of the DIC method is evaluated.