Research Cluster: Wave Propagation and Imaging in Random Media (September 6 - October 13, 2017)

Description

Wave propagation and imaging in complex environments is an important topic in applied mathematics with a wide range of applications, including not only radar and seismic reconstruction but also many others, such as laser beam propagation through clouds, light propagation through the atmosphere in astronomy, secure communications in scattering media, medical imaging, and nondestructive evaluation of materials. This cluster will involve contemporary topics on waves in random media. Recent progress in this area has been motivated on the one hand by a range of applications that involve partly or fully incoherent waves, such as time reversal, active-array imaging, passive imaging and hybrid imaging, and on the other hand by advances in sensor technology that have brought new and massive amounts of data.

Mathematically, the problem of waves in random media may be placed in a stochastic framework, where the complex environments are realizations of random fields and the scattering regimes are determined by important physical scales, such as the wavelength, the distance of propagation, and the scale of the fluctuations. The theory for waves in random media is concerned in particular with describing the statistics of the wave field in a concise manner. It is fundamental to applications in imaging through complex environments.

This cluster brings together scientists with expertise in stochastic analysis and theoretical, numerical, and experimental wave propagation and imaging, random matrix theory, and compressed sensing with the goal of exchanging ideas and advancing the field. The main topics of interest are:

  • Theoretical and numerical studies of wave propagation in random media in a variety of scattering regimes and setups.
  • Inverse source problems and inverse scattering problems in random media.
  • Imaging with distributed and opportunistic noise sources.
  • Applications of random matrix theory for improved detection and imaging in strong random media.
  • Imaging of sparse scenes and connections to compressed sensing.
  • Time dependent problems, where the medium or the scatterers to be imaged are in unknown motion.

Organizing Committee

  • Alexandre Aubry
    (ESPCI Paris Tech)
  • Liliana Borcea
    (University of Michigan)
  • Albert Fannjiang
    (University of California at Davis)
  • Knut Solna
    (University of California at Irvine)
  • Chrysoula Tsogka
    (University of Crete)

= speaker

SCHEDULE HERE
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Research Cluster: Mathematical and Computational Aspects of Radar Imaging

Research Cluster: Mathematical and Computational Aspects of Radar Imaging (October 2 - November 3, 2017)

Description

Radar imaging is a highly developed field that involves a rich variety of mathematical and computational areas, such as electromagnetic theory and partial differential equations, functional analysis, harmonic analysis, coding theory, Lie groups, and statistical signal processing. Still, many challenges remain. For example, more of the physics needs to be incorporated into solutions to the radar inverse problem, including physical scattering mechanisms, multiple scattering, moving objects, and corrections for propagation through random or complex media. Recent hardware developments make it possible to collect an unprecedented amount of data, sampled at extremely high rates and often including polarimetry, and mathematical techniques are needed for fast, accurate image formation and interpretation of this data. Seismology is faced with many similar mathematical problems; this program provides an opportunity for synergistic development of both fields.

This cluster will bring together laboratory scientists and academic researchers with the overarching goal of advancing the field of radar imaging. Particular attention will be paid to exploring mathematical commonalities between radar and seismic imaging and to possibilities for applying seismic imaging techniques to radar imaging. Specific topics of interest include:

  • Statistical methods, including detection theory.
  • Imaging moving targets, including moving targets such as wind turbines.
  • Imaging extended targets, particularly those with direction-dependent and polarization-dependent reflectivities.
  • Imaging under conditions of multiple scattering, including within the target, within the environment, and between both.
  • Extraction of information from radar data & radar images, including identification of objects, terrain, and material properties, and identification of activity.
  • Waveform design, and application of seismic techniques in the radar context.

Organizing Committee

  • Margaret Cheney
    (Colorado State University)
  • Armin Doerry
    (Sandia National Laboratories)
  • Eric Mokole
    (U.S. Naval Research Laboratory (ret.))
  • Frank Robey
    (MIT Lincoln Laboratory)
  • Ed Zelnio
    (Air Force Research Laboratory)

= speaker

Workshop Schedule and Supporting Materials

SCHEDULE HERE
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Research Cluster: Wave Propagation and Inversion in Seismic Applications

Research Cluster: Wave Propagation and Inversion in Seismic Applications (October 23 - November 21, 2017)

Description

Seismic inversion is the process of transforming seismic data generated by active or passive sources into a quantitative description of the subsurface properties of the earth. It addresses important problems related to our energy needs, to hazards such as earthquakes and volcanic eruptions, and to the general study of Earth's interior on a planetary scale. It draws extensively from the mathematical sciences by applying tools from signal processing, elastic and electromagnetic theory, partial differential equations, harmonic analysis, inverse-problem theory, numerical analysis, optimization, and statistics. The sheer volume of seismic data also makes it arguably the oldest area with "big data." Theoretical and engineering developments have advanced this field tremendously in the past several decades; however, there remain many fundamental open questions, ranging from uniqueness and uncertainty through the nonlinear nature of these problems.

This cluster will bring together academic and industrial researchers with the goal of addressing some of the key challenges in the analysis of inverse problems, with emphasis on reconstruction, big data and fast algorithms. Thematic topics include:

  • Fast and massively parallel algorithms for the propagation and scattering of seismic waves, direct and iterative solvers and preconditioners, source dynamics.
  • Stability analysis of seismic inverse problems and optimization, referred to as full waveform inversion in exploration seismology.
  • Numerical techniques cutting across direct and inverse problems: multiscale and spectral finite elements, regularization, numerical homogenization, reduced-order model methods, multiscale time stepping, hybrid methods combining high frequency asymptotics with standard numerical discretization.
  • Direct inverse methods in time-harmonic, time-dependent, and reduced-order model formulations.
  • Data filtering and reduction for imaging a particular target (partial data analysis, redundancy), learning.

Organizing Committee

  • Vladimir Druskin
    (Schlumberger Doll Research)
  • Alison Malcolm
    (Memorial University of Newfoundland)
  • Lexing Ying
    (Stanford University)

= speaker

Workshop Schedule and Supporting Materials

SCHEDULE HERE
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