ASU Scholarship Showcase

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub{Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to nd a subspace approximation to the full problem. Determination of the regularization, parameter for the projected problem by unbiased predictive risk estimation, generalized cross validation, and discrepancy principle techniques is investigated. It is shown that the regularized parameter obtained by the unbiased predictive risk estimator can provide a good estimate which can be used for a full problem that is moderately to severely ill-posed. A similar analysis provides the weight parameter for the weighted generalized cross validation such that the approach is also useful in these cases, and also explains why the generalized cross validation without weighting is not always useful. All results are independent of whether systems are over- or underdetermined. Numerical simulations for standard one-dimensional test problems and two- dimensional data, for both image restoration and tomographic image reconstruction, support the analysis and validate the techniques. The size of the projected problem is found using an extension of a noise revealing function for the projected problem [I. Hn etynkov a, M. Ple singer, and Z. Strako s, BIT Numer. Math., 49 (2009), pp. 669{696]. Furthermore, an iteratively reweighted regularization approach for edge preserving regularization is extended for projected systems, providing stabilization of the solutions of the projected systems and reducing dependence on the determination of the size of the projected subspace.

Mexicans and Mexican Americans have resided in Arizona since the early 16th century. Their history, however, is severely under-documented in the state’s archival repositories. As of 2012, this community is represented in a mere 1-2% of the state’s known archival holdings, and 98% of such documentation is held at Arizona State University’s Chicano/a Research Collection (CRC). This article provides a historical review of the CRC’s establishment in 1970 and how its founding Curator, Dr. Christine Marín, transformed a small circulating book collection into Arizona’s largest repository for Mexican American history. It goes on to examine how the CRC’s sitting Archivist is using social media in tandem with a community-based workshop, bilingual promotional materials and finding aids, and description of unprocessed collections as community outreach and collection development tools in order to remedy the under-documentation of Mexican American history in Arizona. We argue that augmenting traditional archival field collecting methods with these strategies enables the CRC to build a more robust relationship with Arizona’s Mexican American community, allows us to continue expanding our archival holdings, and serves as an example for other repositories seeking to enhance their documentation of marginalized communities.