Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity properties of either the Neumann-to-Dirichlet map (non-linear) or its Fr\'echet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method in the unit disk geometry.Comment: 18 pages, 5 figures, 1 tabl

Kun-dangwok: ''clan lects'' and Ausbau in western Arnhem Land

The sociolinguistic concept of an Ausbau language is widely thought of as exclusively associated with the standardization of languages for the political and social purposes of nation states. Language policy initiated by state institutions, the development of literacy and new specialist registers of language are typical elements involved in the Ausbau process. However, the linguistic ideologies of small language groups such as those of the minority languages of Aboriginal Australia can drive certain forms of deliberate language elaboration. An important aspect of Aboriginal linguistic ideology is language diversity, reflected in the development of elemental sociolinguistic varieties such as patrician lects. In the Bininj Kun-wok dialect chain of western Arnhem Land, a regional system of lectal differentiation known as Kun-dangwok has developed, reflecting an Aboriginal linguistic ideology whereby being different, especially different ways of speaking, are seen as central aspects of identity. The functions of the Kun-dangwok clan led system are described using examples of naturally occurring conversation which provide evidence that clan lects are the result of an Ausbau process that results in the opposite of language standardization and an increase in Abstand between varieties

Sparsity prior for electrical impedance tomography with partial data

This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis coefficients as the penalty term in a Tikhonov functional, and prior information is incorporated by applying a spatially distributed regularization parameter. The resulting optimization problem allows great flexibility with respect to the choice of measurement boundaries and incorporation of prior knowledge. The problem is solved using a generalized conditional gradient method applying soft thresholding. Numerical examples show that the addition of prior information in the proposed algorithm gives vastly improved reconstructions even for the partial data problem. The method is in addition compared to a total variation approach.Comment: 17 pages, 12 figure

Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography

The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the measurement boundary. The observation can be quantified by the concept of distinguishability of inclusions. This paper provides mathematically rigorous results supporting the intuition. Indeed, for a model problem lower and upper bounds on the distinguishability of an inclusion are derived in terms of the boundary data. These bounds depend explicitly on the distance of the inclusion to the boundary, i.e. the depth of the inclusion. The results are obtained for disk inclusions in a homogeneous background in the unit disk. The theoretical bounds are verified numerically using a novel, exact characterization of the forward map as a tridiagonal matrix.Comment: 25 pages, 6 figure

Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented

The regularized monotonicity method: detecting irregular indefinite inclusions

In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet map. Only few reconstruction methods apply when detecting indefinite inclusions, where the conductivity distribution has both more and less conductive parts relative to the background conductivity; one such method is the monotonicity method of Harrach, Seo, and Ullrich. We formulate the method for irregular indefinite inclusions, meaning that we make no regularity assumptions on the conductivity perturbations nor on the inclusion boundaries. We show, provided that the perturbations are bounded away from zero, that the outer support of the positive and negative parts of the inclusions can be reconstructed independently. Moreover, we formulate a regularization scheme that applies to a class of approximative measurement models, including the Complete Electrode Model, hence making the method robust against modelling error and noise. In particular, we demonstrate that for a convergent family of approximative models there exists a sequence of regularization parameters such that the outer shape of the inclusions is asymptotically exactly characterized. Finally, a peeling-type reconstruction algorithm is presented and, for the first time in literature, numerical examples of monotonicity reconstructions for indefinite inclusions are presented.Comment: 28 pages, 7 figure

Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension

The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth dependence can be quantified by the concept of distinguishability of inclusions. This paper considers the distinguishability of perfectly conducting ball inclusions inside a unit ball domain, extending and improving known two-dimensional results to an arbitrary dimension $d \geq 2$ with the help of Kelvin transformations. The obtained depth-dependent distinguishability bounds are also proven to be optimal.Comment: 20 pages, 2 figure

The Design of a new NICU Patient Area: Combining Design for Usability and Design for Emotion

In the design of medical products both usability and emotional experience are important to be considered. Usability can enhance the work situation of medical staff and ensure patient safety. Emotion related product aspects, on the other hand, influence the recovery pace of patients as well as the work satisfaction of staff. For an optimal medical design both aspects should receive well-balanced attention during the design process. Usability and emotional experience are currently related in literature. However, about the relation between these two aspects in practical design projects little information is available. Therefore we will discuss the exploration of the practical relation between Design for Usability and Design for Emotion in a design process. We explored the relation during concurrent application of both design approaches to the design of a patient area for a Neonatal Intensive Care Unit (NICU). Our aim was not to develop a new design method, but to explore in practice how both design approaches could be addressed concurrently. This paper describes the applied design approach, its strength and weaknesses as well as the design results. Overall, the NICU design case has proven that the concurrent application of Design for Emotion and Design for Usability is feasible in practice and results in a satisfactory design. Keywords: Usability; Design For Emotion; Medical Appliance; Participatory Design; Case Study</p