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"Waves generated by opportunistic or ambient noise sources and recorded by passive sensor arrays can be used to image the medium through which they travel. Spectacular results have been obtained in seismic interferometry, which open up new perspectives in acoustics, electromagnetics, and optics. The authors present, for the first time in book form, a self-contained and unified account of correlation-based and ambient noise imaging. In order to facilitate understanding of the core material, they also address a number of related topics in conventional sensor array imaging, wave propagation in random media, and high-frequency asymptotics for wave propagation. Taking a multidisciplinary approach, the book uses mathematical tools from probability, partial differential equations and asymptotic analysis, combined with the physics of wave propagation and modelling of imaging modalities. Suitable for applied mathematicians and geophysicists, it is also accessible to graduate students in applied mathematics, physics, and engineering" [Publisher]

Image processing --- Traitement d'images --- Noise. --- Bruit. --- Green's functions. --- Green, Fonctions de. --- Wave equation. --- Équations d'onde. --- Mathematics. --- Mathématiques.

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Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences. Hence its mathematical understanding is an important issue for today's research. This book provides an introduction to three different topics in partial differential equations arising from applications. The subject of the first course by Michel Chipot (Zurich) is equilibrium positions of several disks rolling on a wire. In particular, existence and uniqueness of and the exact position for an equilibrium are discussed. The second course by Josselin Garnier (Toulouse) deals with problems arising from acoustics and geophysics where waves propagate in complicated media, the properties of which can only be described statistically. It turns out that if the different scales presented in the problem can be separated, there exists a deterministic result. The third course by Otared Kavian (Versailles St.-Quentin) is devoted to so-called inverse problems where one or several parameters of a partial differential equation need to be determined by using, for instance, measurements on the boundary of the domain. The question that arises naturally is what information is necessary to determine the unknown parameters. This question is answered in different settings. The text is addressed to students and researchers with a basic background in partial differential equations.

Differential equations, Partial. --- Partial differential equations

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This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

Elasticity --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Mathematics. --- Properties --- Dirichlet function. --- Helmholtz decomposition theorem. --- Helmholtz decomposition. --- HelmholtzЋirchhoff identities. --- Kelvin matrix. --- Kirchhoff migration. --- Lam system. --- MUSIC algorithm. --- Neumann boundary condition. --- anisotropic elasticity. --- asymptotic expansion. --- asymptotic formula. --- asymptotic imaging. --- ball. --- boundary displacement. --- boundary perturbation. --- boundary value problem. --- boundedness. --- cellular structure. --- compressional modulus. --- crack. --- density parameter. --- direct imaging. --- discrepancy function. --- displacement field. --- displacement. --- elastic coefficient. --- elastic equation. --- elastic inclusion. --- elastic moment tensor. --- elastic structure. --- elastic wave equation. --- elastic wave propagation. --- elastic wave. --- elasticity equation. --- elasticity imaging. --- elasticity. --- ellipse. --- energy functional. --- extended inclusion. --- extended source term. --- extended target. --- far-field measurement. --- filtered quadratic misfit. --- function space. --- gradient scheme. --- hard inclusion. --- hard inclusions. --- heterogeneous shear distribution. --- high contrast coefficient. --- hole. --- imaging functional. --- inclusion. --- incompressible limit. --- internal displacement measurement. --- layer potential. --- linear elasticity. --- linear transformation. --- linearized reconstruction problem. --- measurement noise. --- medium noise. --- nanoparticle. --- nonlinear optimization problem. --- nonlinear problem. --- operator-valued function. --- optimal control. --- potential energy functional. --- pressure. --- radiation condition. --- random fluctuation. --- resolution. --- reverse-time migration. --- scalar wave equation. --- search algorithm. --- shape change. --- shape deformation. --- shape. --- shear distribution. --- shear modulus. --- shear wave. --- small crack. --- small inclusion. --- small-volume expansion. --- small-volume inclusion. --- soft inclusion. --- stability analysis. --- stability. --- static regime. --- stochastic modeling. --- time-harmonic regime. --- time-reversal imaging. --- topological derivative. --- vibration testing.

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This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.

Engineering & Applied Sciences --- Applied Physics --- Mathematics. --- Mathematical physics. --- Mathematical Applications in the Physical Sciences. --- Image processing --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Physical mathematics --- Physics --- Math --- Science