Geometric methods for real-world imaging problems
Eric Miller, Gregory Boverman, Emre Güven, Mohamed Khames ben Hadj Miled, Robin O. Cleveland, Başak Ülker Karbeyaz · The Journal of the Acoustical Society of America · 2006
The extraction of information concerning the internal structure of a medium given sparsely sampled, externally collected data is a ubiquitous problem arising in application areas ranging from the large-scale (geophysical prospecting and environmental remediation) to the small (biomedical imaging and nondestructive evaluation). The sensors used to collect data are equally diverse, encompassing the full spectrum of electromagnetic and mechanical modalities. In spite of the broad variety seen in this class of problems, many share underlying common challenges making the application of core processing methods of potential utility across a range of specific problems. In this talk, we discuss the application of geometric parametrizations to problems we have encountered in geophysical and biomedical imaging problems using optical, ultrasonic, and electromagnetic sensors. Estimating the geometry of a tumor, plume of toxic waste, or lesion created in the process of hyperthermia cancer treatment often reduces the ill-posed nature of the imaging problem and allows for the extraction of parameters directly linked to the application-specific information we seek to recover from the data. We shall discuss three approaches we have used to parametrize shape as well as our experience in applying these methods to real-world data.