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# ACMD Seminar: A Statistical Approach for Ill-Posed Inverse Problems

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Matthew Brown*Virginia Tech*

Friday, November 3, 2017, 15:00 – 16:00	Building 101, Lecture Room C	Gaithersburg

Friday, November 3, 2017, 13:00 – 14:00	Room TBD	Boulder

**Host:** Wesley Griffin

**Abstract:** Inverse problems are said to be ill-posed when they are ill-conditioned or contaminated by noisy observations. Here we investigate iterative methods for large scale ill-posed inverse problems and how they have been generalized to utilize additional information in the form of statistical priors. In particular we will look at methods based on the Generalized Golub-Kahan (GenGK) bidiagonalization procedure. Incorporating the statistical prior information is accomplished via additional matrix-vector products at each iteration, so we will also discuss scenarios where the problem structure can be exploited for computational speedup. Numerical results will be presented from an application in passive seismic tomography.

**Bio:** Matthew Brown is in the final year of his Ph.D. studies in Mathematics at Virginia Tech (VT). He began his graduate education subsequent to a twelve year career in information technology with positions progressing from networking (voice, data, video), to infrastructure and small data-center design, and then IT management. He has a B.S. in Mathematics and Computer Science from High Point University in High Point, NC and a M.S. in Mathematics from VT. The latter years of his graduate studies have been supported by research assistantships working with Advanced Research Computing (ARC) at VT. ARC runs several state-of-the-art distributed computing and visualization clusters which are used by VT's research community and various collaborative partnerships at VT. Currently, Matt serves as the primary ARC contact for the Virginia Department of Environmental Quality's (DEQ) air quality modeling day-to-day operations.

Matt's research has been centered around the numerical solution of large-scale, ill-posed inverse problems with particular applications in imaging such as deblurring and tomography under the advisement of Julianne Chung. His early work in this area was on transpose-free Krylov methods for non-symmetric problems and then on integrating wavelet-based de-noising into general Krylov methods. Current research and developing interests include statistical algorithms and perspectives for inverse problems, efficient numerical techniques (mathematical and/or computational) for very large or dynamic inverse problems, and the application of high performance computing technologies (MPI, GPU) to enable these and other computational techniques at scale.

Information technologyMathematics and statistics

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