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Inverse Problems Seminar

Alan Thomas (Department of Mathematical Sciences, Clemson University)

**Potential Applications of Implicit Processing to Optical
Tomography**

Abstract: We will give an overview of the inverse problem in optical tomography with some common reconstruction schemes. We will follow with some ideas for potential reconstruction algorithms that utilize implicit processing. This talk is intended to stimulate a discussion between experts in image processing and those working in inverse problems.

October 10, 2005, 11:15 am, Lind Hall 229Emad S. Ebbini (Department of Electrical and Computer Engineering, University of Minnesota)

**Post-beamforming Volterra Filter for Ultrasound Pulse-Echo
Imaging**

Several microbubble ultrasound contrast agents (UCA) have been
recently introduced to allow imaging blood perfusion in the
microvasculature. Microbubbles exhibit strong linear and
nonlinear response to incident ultrasonic beams that can be
utilized to increase the contrast-to-tissue ratio (CTR). If
successful, this will lead to functional ultrasonic imaging
methods. This increased interest in UCA imaging has heightened
the need for specialized imaging methods for improving both the
sensitivity and specificity to the agent. For most microbubble
UCAs, the nonlinear behavior of the bubbles led to several
imaging methods with improved CTR by rejecting the linear
tissue response. These developments have already led to the
introduction of specialized imaging methods for UCAs such as
pulse inversion (PI) and contrast phase sequence (CPS) imaging.
Methods like PI and CPS provide elegant solutions to this
problem by utilizing sequences of two or more pulses with
specified phase and amplitude relationships. The fundamental
tissue component can be cancelled by appropriately combining
the echoes from these pulses. Impressive results in a range of
significant clinical applications have already been achieved
with these methods. However, the goal of imaging very small
concentrations of UCA at the microvasculature level has not yet
been achieved. This is largely due to sensitivity to motion and
loss of signal to noise due to cancellation of the (dominant)
fundamental component.
In order to mitigate some of the limitations of multi-pulse
imaging, we have investigated the applicability of an
input-output system identification model based on the
2^{nd} order
Volterra filter (SoVF) to pulse-echo ultrasound. The objective
was to develop a robust method to separate the linear and
quadratic components from pulse-echo data without the need for
multiple transmit pulses. Furthermore, we aimed to establish
that the quadratic component contains all the sum and
difference frequency interactions and not just harmonic
interactions. This has the advantage of preserving all the
spectral components resulting from the UCA activity throughout
the visible spectrum and not limit it to the second harmonic
(SH) generation. In this presentation, we describe the SoVF and
discuss its applicability to acoustic wave propagation in
tissue media. In addition, we describe algorithms for obtaining
the coefficients of the linear and quadratic kernels from
ultrasound pulse-echo radio frequency (RF) imaging data.
Finally, we give illustrative examples from imaging experiments
of UCA in flow phantoms as well as *in vivo* data. Comparisons
with established methods such as SH and harmonic PI are also
presented and discussed.

Gary Margrave (Consortium for Research in Elastic Wave Exploration Seismology, University of Calgary)

**Seismic Imaging using Wavefield Extrapolation**

pdf

I will begin with an overview of seismic imaging as it is currently practiced and show a variety of current images. Then I will discuss some of the research challenges whose solution might lead to images with better resolution or higher reliability. Finally, I will briefly discuss the application of gabor frames and pseudodifferential operator concepts to seismic imaging and show two examples useful research results in this regard.

October 24, 2005, 11:15 am, Lind Hall 409

Rachael Brady (Department of Computer Science, Duke University)

** Tutorial on visualization techniques appropriate for
imaging data**

The demand for advanced imaging techniques continues to grow in many disciplines (biological, medical, seismic, radar), across many scales (nano to astrophysical), covers different frequencies (x-ray, optical) and dimensions. The process of imaging involves both the mathematician, to develop the models, and the domain scientist, to interpret and validate the models. Most scientists are very familiar with validating their data through common visual techniques such as plots and 2D image slices. WIth the advent of 3D and higher imaging methods it can be useful to apply more sophisticated visualization techniques both during development of a new model and for interpreting the resulting data. This talk will present an overview of visualization techniques organized