On Algorithms Based on Joint Estimation of Currents and Contrast in Microwave Tomography

This paper deals with improvements to the contrast source inversion method which is widely used in microwave tomography. First, the method is reviewed and weaknesses of both the criterion form and the optimization strategy are underlined. Then, two new algorithms are proposed. Both of them are based on the same criterion, similar but more robust than the one used in contrast source inversion. The first technique keeps the main characteristics of the contrast source inversion optimization scheme but is based on a better exploitation of the conjugate gradient algorithm. The second technique is based on a preconditioned conjugate gradient algorithm and performs simultaneous updates of sets of unknowns that are normally processed sequentially. Both techniques are shown to be more efficient than original contrast source inversion.Comment: 12 pages, 12 figures, 5 table

Identification de courants équivalents sur un circuit numérique à haut débit à partir de mesures en champ proche

Mesures en champ proche -- Problèmes mal posés et régularisation -- Mesures en champ proche appliquées aux circuits numériques -- Régularisation appliquée aux distributions de courants -- Identification des courants à partir de mesures réelles et extrapolation du champ lointain -- Sources d'erreurs et travaux futurs

DÉVELOPPEMENT D'ALGORITHMES D'INVERSION RAPIDES ET PROPOSITIONS RELATIVES À LA CONFIGURATION DU MONTAGE DE MESURES DANS UN CONTEXTE DE TOMOGRAPHIE MICRO-ONDES APPLIQUÉE À LA DÉTECTION DU CANCER DU SEIN

This thesis is about microwave tomography applied to breast cancer detection. Both algorithmic aspects and questions related to the configuration of the measurements setup are treated.The time needed for the reconstruction process is critical if clinical applications of microwave tomography are envisioned. In the first part of the thesis, we suggest new algorithms designed to decrease the calculation time in comparison with the concurrent methods. The “current source inversion” (CSI) method is used as starting point of the reflection. We first identify some of its pitfalls and propose two generalized versions, which are faster and more robust. Then, two new families of methods, which focus on different bottlenecks of the generalized CSIs, are introduced. They are based on two new formulations of the forward problem. The first of these is mathematically equivalent to the one used by CSI while the second one is based on approximations.Regarding the configuration of the measurements setup, we first show that the resolution of the reconstructed images can be significantly improved by compressing the breast. We also propose a new setup based on the properties of the dielectric waveguides. Measurements can then be performed in the air rather than in a match liquid. This opens the door to the development of more compact setups.Cette thèse porte sur la tomographie micro-ondes appliquée à la détection du cancer du sein. Les aspects algorithmiques ainsi que ceux reliés à la configuration du montage de mesure y sont traités.Le temps nécessaire à la reconstruction d'une image étant critique pour d'éventuelles applications cliniques de la tomographie micro-ondes, nous proposons, en première partie, une série d'algorithmes qui offrent un coût de calcul diminué par rapport aux méthodes concurrentes. La méthode « current source inversion » (CSI) est utilisée comme point de départ de la réflexion. On identifie certaines faiblesses de cet algorithme et on en propose deux généralisations, plus rapides et plus robustes. Deux nouvelles familles de méthodes, s'attaquant à différents goulots d'étranglement des méthodes CSI généralisées, sont aussi proposées. Elles sont basées sur deux nouvelles formulations du problème direct. La première est mathématiquement équivalente à celle d'origine alors que la seconde est basée sur des approximations.En ce qui a trait à la configuration du montage de mesures, on montre que la résolution des images reconstruites peut être significativement améliorée en ayant recours à la compression du sein. On propose aussi un montage qui exploite les propriétés des guides d'ondes diélectriques. Celui-ci permet de mesurer le champ dans l'air plutôt que dans un liquide d'adaptation, ce qui ouvre la porte au développement de montages plus compacts

Contrast source inversion method applied to relatively high contrast objects

International audienceThis paper presents a contrast source inversion method for microwave tomography with improved performance with respect to the popular multiplicative regularized contrast source inversion (MR-CSI) method when the contrast of the object under study is relatively high. More precisely, some shortcomings of MR-CSI which may prevent it from performing adequately on higher contrast objects are outlined. The proposed method does not suffer from such shortcomings, but necessitates the tuning of parameters. However, a unique set of parameters can be used in a wide variety of experimental conditions related to a given application. Simple guidelines to determine their values are provided

Fast solutions of the 2D inverse scattering problem based on a TSVD approximation of the internal field for the forward model

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A 3-TERM OPTIMIZATION CRITERION FOR FASTER INVERSION IN MICROWAVE TOMOGRAPHY

The problem of microwave tomography consists of finding the electrical characteristics (permittivity and conductivity) of a medium using scattered fields measured under various conditions of illumination. Such inversion can be achieved with a variety of techniques based upon the minimization of an appropriate criterion. The popular current source inversion (CSI) technique is one of those. In this paper, the CSI technique is presented and its main limitations are underlined. Then, in order to overcome these limitations, a generalized form of CSI is developed. An analysis of the time consuming operations of this new algorithm is done, and a new technique is proposed; it proves to be faster than the other two methods, the speed increase ranging between factors of 2 and 5. Performance of the algorithms is illustrated with examples based on synthetic data