The investigator and her postdoctoral fellow together with one graduate student are focusing their research for this grant on the development, analysis and implementation of novel algorithms for solution of linear ill-posed inverse problems in which both the measured data and the model are error-contaminated. The analysis will provide improved insight for the performance of new and existing algorithms. One direction is analysis of the linear support vector machine which has already been validated as an effective tool in statistical pattern recognition. Reformulation of the support vector machine to account for errors that may occur in the features of the patterns to be classified, an example of which might be error contaminated microarray data, utilizing the tools of regularized total least squares, will better account for these errors in data measurements. Another direction is the use of a total variation regularized structured total least squares algorithm to provide a completely new mechanism for combining edge preserving regularization with an errors in the variables model of signal inversion. For multiple, but similarly corrupted, signals, a concurrent solution technique will enhance signal inversion and restoration. While several approaches for Tikhonov regularized total least squares have been presented in literature, an effective comparison of their competitiveness for both synthetic and real data has not been performed. These investigators will determine which of algorithms are most suitable for extensions to realistic problems. All software developed for this project will be disseminated to collaborators for their applications and published on the world wide web.
The investigators have a track record of studying and developing computational tools which can be utilized for many different applications. The successful outcome of this particular research will have major impact on solution of so-called inverse problems for biomedical applications, genetic data analysis and seismic tomography. These are areas in which the PI is actively collaborating with other practioners, including those at the Translational Genomics Research Center in Phoenix, AZ. Inverse problems arise in many biomedical situations: for example medical imaging can be used to obtain non-invasive information about the function of an internal organ, potentially also impacted by presence of malignant or benign tumor. Another direction is for the design of new and improved analysis of seismic data with the intent to lead to increased understanding of the dynamic nature of the Earth's interior, and in particular the relationship between plate tectonic processes observed at the surface and the thermo-chemical structure of the interior.
