Solving inverse electromagnetic scattering problems via domain derivatives

We employ domain derivatives to solve inverse electromagnetic scattering problems for perfect conducting or for penetrable obstacles. Using a variational approach, the derivative of the scattered field with respect to boundary variations is characterized as the solution of a boundary value problem of the same type as the original scattering problem. The inverse scattering problem of reconstructing the scatterer from far field measurements for a single incident field can thus be solved via a regularized iterative Newton scheme. Both the original forward problem and the problem characterizing the domain derivative are formulated as boundary integral equations and we carefully describe how these formulations are obtained in the case of Lipschitz domains. The integral equations are solved using the boundary element library Bempp. A number of numerical examples of shape reconstructions are presented

Accuracy of end-on fluoroscopy in predicting implant position in relation to the vertebral canal in dogs.

Objective To evaluate the accuracy of end-on fluoroscopy in predicting implant position in relation to the vertebral canal in the canine thoracolumbar vertebral column. Study design In vitro imaging and anatomic study. Animals Canine cadaveric thoracolumbar vertebral columns (n = 5). Methods Smooth Steinmann pins were inserted bicortically into the thoracolumbar vertebral columns between T10 and L7 using recommended insertion angles. Penetration of the spinal canal was not strictly avoided. After pin placement, end-on fluoroscopy images were obtained of each pin. Pin position was subsequently assessed by four evaluators and determined to either being out of the vertebral canal or in, with the latter being additionally divided into partially or completely penetrating the canal. To assess potential differences in modalities, fluoroscopy images were gray-scale inverted and evaluated again later by the same four individuals. Correct identification of pin position in relationship to the vertebral canal was assessed for both fluoroscopy images. Anatomic preparation of the spines was used for verification of pin position in relation to the spinal canal. Some data from this study were compared with historical data on accuracy using orthogonal radiography and computed tomography (CT). Results Overall sensitivity and specificity of F to detect vertebral canal penetration was 98.8 % (95% confidence interval (CI), 96.0-99.6) and 98.0% (95% CI, 77.0-99.9), respectively. For Fi, sensitivity and specificity were 97.0% (95% CI, 91.5-99.0) and 98.5% (95% CI, 81.5-99.9) respectively. F exceeded Fi for the sensitivity of detecting pin penetration into the vertebral canal (p = 0.039) but specificities were not different (p = 0.585). When comparing to historical data, the overall accuracy of end-on fluoroscopy (F) and inverted fluoroscopy (Fi) was statistical better than conventional radiographic assessment (p < 0.001). Conclusion End-on fluoroscopy is a highly accurate method for the assessment of pin position in relationship to the thoracolumbar spinal canal in cadaveric dogs. Clinical significance End-on fluoroscopy, with or without inversion, is accurate in identifying vertebral canal violation by bicortically placed Steinmann pins. When CT is not available, end-on fluoroscopy might be a valuable imaging modality to determine pin position in the canine vertebral column

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Atypical cellular elements of unknown origin in the subbasal nerve plexus of a diabetic cornea diagnosed by large-area confocal laser scanning microscopy

In vivo large-area confocal laser scanning microscopy (CLSM) of the human eye using EyeGuidance technology allows a large-scale morphometric assessment of the corneal subbasal nerve plexus (SNP). Here, the SNP of a patient suffering from diabetes and associated late complications was analyzed. The SNP contained multiple clusters of large hyperintense, stellate-shaped, cellular-like structures. Comparable structures were not observed in control corneas from healthy volunteers. Two hypotheses regarding the origin of these atypical structures are proposed. First, these structures might be keratocyte-derived myofibroblasts that entered the epithelium from the underlying stroma through breaks in Bowman’s layer. Second, these structures could be proliferating Schwann cells that entered the epithelium in association with subbasal nerves. The nature and pathophysiological significance of these atypical cellular structures, and whether they are a direct consequence of the patient’s diabetic neuropathy/or a non-specific secondary effect of associated inflammatory processes, are unknown

An inverse source problem for the heat equation and the enclosure method

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given.Comment: 23page

Shape optimization for the generalized Graetz problem

We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared

A Second Degree Method for Nonlinear Inverse Problems

: The paper is concerned with the solution of nonlinear ill-posed problems by methods that utilise the second derivative. A general predictor--corrector approach is developed; one which avoids solving quadratic equations during the iteration process. Combining regularisation of each iteration step with an adequate stopping condition leads to a general regularisation scheme for nonlinear equations. Possible implementations and discussion of the performance of this method are illustrated by applications to some well--known inverse problems. Keywords: Nonlinear ill--posed problems, iterative regularisation methods, domain derivative AMS subject classification: 35R30, 65J15, 65J20 1 Introduction In inverse problems we are often concerned with solving the nonlinear equation F (x) = g; (1.1) where F : U ` X ! Y is a differentiable operator between Hilbert spaces; those relating the unknown x (in our viewpoint, a coefficient in a partial differential operator) and the data g (typically so..