Jeffrey Donatelli

Summary of Research:

With advances in imaging technology, we are able to view our universe at increasingly smaller scales. Currently, next generation systems are being designed to determine the three dimensional molecular structure of individual particles. However, these systems require a new class of sophisticated computational algorithms to process their collected data into meaningful images.

Two current popular approaches to single particle imaging are x-ray diffraction and cryo-electron microscopy. In each case, a powerful beam of either x-rays or electrons is shot at a particle, yielding an image pattern. However, the beam energy density required to obtain molecular resolution is high enough to actually destroy the object being observed and, thus, one is only able to gather information from a single orientation for each particle being imaged. Therefore, in practice, one attempts to gather a large sample of identical particles and image them at different orientations. However, these samples are likely contaminated with other undesired objects, and one also has no control over nor a priori knowledge of the orientations. Furthermore, due to quantum effects, large statistical fluctuations occur in this process, which yield extremely noisy images, typically with a signal to noise ratio on the order of 1%.

While some techniques have been developed to tackle these problems individually, a full study encompassing both theory and treatment of real physical data has not yet come full circle. For one, much is still unknown about the type of noise involved and whether currently proposed imaging algorithms are robust enough to handle it. Additionally, in order to obtain sufficient resolution, one has to analyze potentially hundreds of millions of images per object to be imaged. Thus, a feasible complete numerical methodology must solve the associated denoising, classification, orientation recovery, and image inverse problems with extreme robustness to noise and must scale on the massively parallel machines of the future.

Publications:

-Benedetto, J.J.; Donatelli, J.; Konstantinidis, I.; Shaw, C., A Doppler statistic for zero autocorrelation waveforms, 2006 40th Annual Conference on Information Sciences and Systems, March 2006 Page(s):1403 - 1407.

-Benedetto, John J. ; Donatelli, Jeffrey ; Konstantinidis, Joannis ; Shaw, Christopher, Zero Autocorrelation Waveforms: A Doppler Statistic and Multifunction Problems, ICASSP 2006 Proceedings. 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, 2006. May 2006, Volume: 5, On page(s): V-V.

-Benedetto, J.J.; Donatelli, J.J., Ambiguity Function and Frame-Theoretic Properties of Periodic Zero-Autocorrelation Waveforms, IEEE Journal of Selected Topics in Signal Processing, Volume 1, Issue 1, June 2007 Page(s):6 - 20.

-Benedetto, J.J.; Donatelli, J.J, Frames and a Vector Valued Ambiguity Function, Asilomar Conference on Signals, Systems, and Computers, October 2008.

-Benedetto, J.J.; Donatelli, J.J., Ambiguity functions for vector-valued periodic codes, to be submitted.

Awards:

-Presidential Scholarship, 2003-2007
-Semester Academic Honors, 2003-2007
-Vigre Grant, 2005-2007
-University Honors Citation, 2004
-Strauss Teaching Assistant, 2005-2006
-Aziz Mathematical Scholarship, 2006-2007
-Outstanding Senior Award (Mathematics), 2007
-High Honors in Mathematics, 2007
-NSF Graduate Research Fellowship (Declined), 2009