Source Localization by Gradient Estimation Based on Poisson Integral

International audienceWe consider the problem of localizing the source of a diffusion process. The source is supposed to be isotropic, and several sensors, equipped on a vehicle moving without position information, provide pointwise measures of the quantity being emitted. The solution we propose is based on computing the gradient -- and higher-order derivatives such as the Hessian -- from Poisson integrals: in opposition to other solutions previously proposed, this computation does neither require specific knowledge of the solution of the diffusion process, nor the use of probing signals, but only exploits properties of the PDE describing the diffusion process. The theoretical results are illustrated by simulations

Source localization using Poisson integrals

International audienceThis paper deals with the problem of source localization in diffusion processes via several sensor devices providing pointwise concentration measures; sensors are assumed to be arranged in circular arrays, they can be fixed along the array or they can turn along a circular path defined by the array. The originality of the proposed source localization solution lies in the computation of the gradient and of higher-order derivatives (i. e., the Hessian) from Poisson integrals; in opposition to other solutions published in the literature, this computation does neither require specific knowledge of the solution of the difiusion process, nor the use of probing signals, but only exploits properties of the PDE. The Laplacian of the measured value is null on the studied domain; such an assumption is justified for isotropic diffusive sources in steady-state. The paper also presents some simulation results of a source-seeking torque control law for mobile non-holonomic robots looking for a heat source in a room, where the source is modeled as a small circular region

The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body

First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we describe in detail. We use a modular algorithm that is designed to avoid a posteriori selection effects, automatically picking out the most promising signals, performing a search for causal boundaries, and conducting a full Bayesian parameter estimation and model selection analysis. We outline each component of this algorithm, describing its response to simulated CMB skies with and without bubble collisions. Comparing the results for simulated bubble collisions to the results from an analysis of the WMAP 7-year data, we rule out bubble collisions over a range of parameter space. Our model selection results based on WMAP 7-year data do not warrant augmenting LCDM with bubble collisions. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.Comment: Companion to arXiv:1012.1995. 41 pages, 23 figures. v2: replaced with version accepted by PRD. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchange

Distributed Source Seeking without Global Position Information

International audienceWe present a distributed control law to steer a group of autonomous communicating sensors towards the source of a diffusion process. The graph describing the communication links between sensors has a time-invariant topology, and each sensor is able to measure (in addition to the quantity of interest) only the relative bearing angle with respect to its neighbour, but has no absolute position information and does not know any relative distance. Using multiple sensors is useful in wide environments (e.g., under the sea), or when the function describing the diffusion process is slowly changing in space, so that a single sensor may have to travel long distances before having a good gradient estimation. Our approach is based on a twofold control law, which is able to bring and keep the set of sensors on a circular equispaced formation, and to steer the circular formation towards the source via a gradient-ascent technique. The effectiveness of the proposed algorithm is both theoretically proven and supported by simulation results

Reduced and coded sensing methods for x-ray based security

Current x-ray technologies provide security personnel with non-invasive sub-surface imaging and contraband detection in various portal screening applications such as checked and carry-on baggage as well as cargo. Computed tomography (CT) scanners generate detailed 3D imagery in checked bags; however, these scanners often require significant power, cost, and space. These tomography machines are impractical for many applications where space and power are often limited such as checkpoint areas. Reducing the amount of data acquired would help reduce the physical demands of these systems. Unfortunately this leads to the formation of artifacts in various applications, thus presenting significant challenges in reconstruction and classification. As a result, the goal is to maintain a certain level of image quality but reduce the amount of data gathered. For the security domain this would allow for faster and cheaper screening in existing systems or allow for previously infeasible screening options due to other operational constraints. While our focus is predominantly on security applications, many of the techniques can be extended to other fields such as the medical domain where a reduction of dose can allow for safer and more frequent examinations. This dissertation aims to advance data reduction algorithms for security motivated x-ray imaging in three main areas: (i) development of a sensing aware dimensionality reduction framework, (ii) creation of linear motion tomographic method of object scanning and associated reconstruction algorithms for carry-on baggage screening, and (iii) the application of coded aperture techniques to improve and extend imaging performance of nuclear resonance fluorescence in cargo screening. The sensing aware dimensionality reduction framework extends existing dimensionality reduction methods to include knowledge of an underlying sensing mechanism of a latent variable. This method provides an improved classification rate over classical methods on both a synthetic case and a popular face classification dataset. The linear tomographic method is based on non-rotational scanning of baggage moved by a conveyor belt, and can thus be simpler, smaller, and more reliable than existing rotational tomography systems at the expense of more challenging image formation problems that require special model-based methods. The reconstructions for this approach are comparable to existing tomographic systems. Finally our coded aperture extension of existing nuclear resonance fluorescence cargo scanning provides improved observation signal-to-noise ratios. We analyze, discuss, and demonstrate the strengths and challenges of using coded aperture techniques in this application and provide guidance on regimes where these methods can yield gains over conventional methods