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Register a new userFocusing inversion techniques applied to electrical resistance tomography in an experimental tank
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We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in using a priori information about targets to reduce the ambiguity and the instability of the solution. By using the minimum gradient support (MGS) stabilizing functional, we introduce the following geometrical prior information in the reconstruction process: anomalies have sharp boundaries. The presented work is embedded in a project (L.A.R.A.) which aims at the estimation of hydrogeological properties from geophysical investigations. L.A.R.A. facilities include a simulation tank (4 m x 8 m x 1.35 m); 160 electrodes are located all around the tank and used for 3-D ERT. Because of the large number of electrodes and their dimensions, it is important to model their effect in order to correctly evaluate the electrical system response. The forward modelling in the presented algorithm is based on the so-called complete electrode model that takes into account the presence of the electrodes and their contact impedances. In this paper, we compare the results obtained with different regularizing functionals applied on a synthetic model.
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Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed problem. In the framework of Tikhonov regularization theory, in order to replace an ill-posed problem by a well-posed one and to get a unique and stable solution, a stabilizing functional (stabilizer) has to be introduced. The stabilizer selects the desired solution from a class of solutions with a specific physical and/or geometrical property; e.g., the existence of sharp boundaries separating media with different petrophysical parameters. Usually stabilizers based on maximum smoothness criteria are used during the inversion process; in these cases the solutions provide smooth images which, in many situations, do not describe the examined objects properly. Recently a new algorithm of direct minimization of the Tikhonov parametric functional with minimum support stabilizer has been introduced; it produces clear and focused images of targets with sharp boundaries. In this research we apply this new technique to real radar tomographic data and we compare the obtained result with the solution generated by the more traditional minimum norm stabilizer.
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $ell_2$ penalties are compared to so-called sparsity promoting $ell_1$ and $ell_0$ penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an $ell_2$ norm works almost as well as minimizing the total variation but is much more efficient. If gradients (edges of anomalies) should be resolved with a minimum of distortion, we prefer $ell_1$ damping of Daubechies-4 wavelet coefficients. It has the additional advantage of yielding a noiseless reconstruction, contrary to simple $ell_2$ minimization (`Tikhonov regularization) which should be avoided. In some of our examples, the $ell_0$ method produced notable artifacts. In addition we show how nonlinear $ell_1$ methods for finding sparse models can be competitive in speed with the widely used $ell_2$ methods, certainly under noisy conditions, so that there is no need to shun $ell_1$ penalizations.
Magnetic resonance-electrical properties tomography (MR-EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available, however all these methods present several limitations which hamper the clinical applicability. Standard Helmholtz based MR-EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion-EPT (CSI-EPT) are typically time consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, i.e. using MR-EPT or DL-EPT as initialization guesses for standard 3D CSI-EPT. Using realistic electromagnetic simulations at 3 T and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared to standard 3D CSI-EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL-EPT reconstruction followed by a 3D CSI-EPT reconstruction would be beneficial. DL-EPT combined with standard 3D CSI-EPT exploits the power of data driven DL-based EPT reconstructions while the subsequent CSI-EPT facilitates a better generalization by providing data consistency.
Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new algorithmic structure provides additional benefits to pCT image quality. Structural and parametric changes introduced to the original TVS algorithm included: (1) inclusion or exclusion of TV reduction requirement, (2) a variable number, $N$, of TV perturbation steps per feasibility-seeking iteration, and (3) introduction of a perturbation kernel $0<alpha<1$. The structural change of excluding the TV reduction requirement check tended to have a beneficial effect for $3le Nle 6$ and allows full parallelization of the TVS algorithm. Repeated perturbations per feasibility-seeking iterations reduced total variation (TV) and material dependent standard deviations for $3le Nle 6$. The perturbation kernel $alpha$, equivalent to $alpha=0.5$ in the original TVS algorithm, reduced TV and standard deviations as $alpha$ was increased beyond $alpha=0.5$, but negatively impacted reconstructed relative stopping power (RSP) values for $alpha>0.75$. The reductions in TV and standard deviations allowed feasibility-seeking with a larger relaxation parameter $lambda$ than previously used, without the corresponding increases in standard deviations experienced with the original TVS algorithm. This work demonstrates that the modifications related to the evolution of the original TVS algorithm provide benefits in terms of both pCT image quality and computational efficiency for appropriately chosen parameter values.
Seismic vulnerability analysis of existing buildings requires basic information on their structural behaviour. The ambient vibrations of buildings and the modal parameters (frequencies, damping ration and modal shapes) that can be extracted from them naturally include the geometry and quality of material in the linear elastic part of their behaviour. The aim of this work is to use this modal information to help the vulnerability assessment. A linear dynamic modal model based on experimental modal parameters is proposed and the fragility curve corresponding to the damage state ?Slight? is built using this model and a simple formula is proposed. This curve is particularly interesting in moderate seismic areas. This methodology is applied to the Grenoble City where ambient vibrations have been recorded in 61 buildings of various types and to the Pointe-`a-Pitre City with 7 study-buildings. The fragility curves are developed using the aforementioned methodology. The seismic risk of the study-buildings is discussed by performing seismic scenarios.
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