Our research proposal deals with the development of a highly parallelizable, spatial, limited angle model for computerized X-ray and electron tomography, capable to perform spatial reconstructions in real time. This model is based upon a continuous extension of the Radon transform on vector spaces over finite fields. The limited angle feature of this model is specially important in three-dimensional imaging with transmission electron microscopes where the tilting angle is limited to +/-60 degrees. It is also important in the design of scanning devices for X-ray tomography since it.would permit to eliminate the tunnel shape of current scanners. The first phase of the proposed research, regarding X-ray tomography, is two-fold. First, following previous findings, we shall complete the study by determining the geometry that yields minimum noise, and accordingly, we shall adjust the algorithms for simulating how the model works in the spatial case, under sequential and parallel programming. Secondly, a comparative study of the quality of the reconstructions and speed will be performed, taking into consideration other existing models. The second phase consist of a new specific aim of this project related to electron tomography, namely, to apply a modification of our algorithm to data collected by using transmission electron microscopy, following a recent technique developed by P. Schwander (AT&T Bell Labs.) to determine the atomic structure of crystals. Schwander's methods have open a new field which could be named Discrete Binary Tomography, in which our algorithms seem to work well. Indeed, in case that the crystal consists of one type of atom, a crystal can be model as a three dimensional array only of 0's and 1's of which it is possible to measure projection only in two to four directions along certain zone axes. Therefore, the heuristic consists in applying our reconstruction transform to the available projections obtaining a 3-dim array of values. Each of these values, measured on a scale from 0.0 to 1.0, gives the likelihood of the presence of an atom in that position. Some preliminary algorithms developed following this heuristic are yielding promising reconstructions. An important goal of this project is to attract two outstanding graduate minority students majoring in mathematics or in computer sciences, to biomedical research. For at least three years these students will receive personalized training in the mathematics of tomography, will be encouraged to pursue doctoral studies in bio- mathematics, and will be on charge of most of the computational development and implementation of the model. The long-term objectives of this proposal are to create a multi- disciplinary environment, involving graduate minority students, mathematicians, computer scientists, engineers and physicists, aimed at producing biomedical research in the various aspects of tomography, such as a prototype X-ray CT scanner based on our spatial model.
| Ramírez-Camejo, Luis A; Maldonado-Morales, Génesis; Bayman, Paul (2017) Differential Microbial Diversity in Drosophila melanogaster: Are Fruit Flies Potential Vectors of Opportunistic Pathogens? Int J Microbiol 2017:8526385 |
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| Huang, Qing; Quiñones, Edwin (2016) A spectroscopic method to determine the activity of the restriction endonuclease EcoRV that involves a single reaction. Anal Biochem 497:103-5 |
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| Ramírez-Camejo, Luis A; Torres-Ocampo, Ana P; Agosto-Rivera, José L et al. (2014) An opportunistic human pathogen on the fly: strains of Aspergillus flavus vary in virulence in Drosophila melanogaster. Med Mycol 52:211-9 |
| Galindo-Cardona, Alberto; Acevedo-Gonzalez, Jenny P; Rivera-Marchand, Bert et al. (2013) Genetic structure of the gentle Africanized honey bee population (gAHB) in Puerto Rico. BMC Genet 14:65 |
| Santiago-Rodriguez, Tasha M; Rivera, Jessica I; Coradin, Mariel et al. (2013) Antibiotic-resistance and virulence genes in Enterococcus isolated from tropical recreational waters. J Water Health 11:387-96 |
| Pantoja-Feliciano, Ida Gisela; Clemente, Jose C; Costello, Elizabeth K et al. (2013) Biphasic assembly of the murine intestinal microbiota during early development. ISME J 7:1112-5 |
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