Inverse Problems Seminar: Direct Methods for Shear Modulus Inversion
Inverse Problems Seminar
Direct methods for shear modulus inversion in the time-harmonic viscoelastic scalar wave model
Quinn Kolt
Applied Mathematics BS Student
Computer Science Student
School of Mathematical Sciences, RIT
Abstract:
Shear-wave elasticity imaging is a modern approach for the noninvasive identification of diseased soft tissue. This technique is performed by first measuring the propagation of artificially generated shear waves through the tissue and then reconstructing the corresponding shear modulus from the measured displacement. We seek to identify accurate and efficient methods for this reconstruction. As a continuation of the previous talk, I develop five direct methods for shear modulus inversion in the scalar wave problem. I derive the variational formulations for each of these methods and then compare them with synthetic examples.
Speaker Bio:
Quinn Kolt is an undergraduate double major in applied mathematics and computer science. They have performed research in inverse problems since the start of 2019. They spent two summers working on stochastic methods for solving elliptic inverse problems with random noise. This past fall semester, they studied various deterministic methods for the scalar wave inverse problem. They will graduate with a BS in December and pursue a PhD in operator algebras.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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