Xiang-Gen Xia
University of Delaware, DE·Engineering
Radar, hyperspectral cameras and medical sensors produce huge multidimensional datasets. Time, storage, bandwidth and computing power are all limited, so these data are hard to capture, process and store.
- Fields
Engineering
Mathematics & Statistics
Computer Science
- Topics
Chinese remainder theorem
robust CRT
integer matrices
- Grants
- 1 known grant, through Jul 2027
What they work on
- Develop a systematic theory of the multidimensional Chinese remainder theorem (MD-CRT) and its error-tolerant robust version for general sets of integer matrix moduli, beyond commuting matrix pairs.
- Extend MD-CRT and robust MD-CRT to recover a single real-valued vector, as well as multiple integer or real vectors, from their remainders.
- Apply robust MD-CRT to recover vector-valued signals from multi-channel modulo analog-to-digital converters (ADCs) and to radar target detection.
- Use MD-CRT methods to detect moving targets and estimate their motion in synthetic aperture radar (SAR) imaging with planar antenna arrays.
More about the research
An old piece of number theory, the Chinese remainder theorem (CRT), can help. It recovers a large number from its remainders after dividing by several small numbers, called moduli. This lets a big task be split into small independent pieces that run in parallel, and it can also help radar detect targets. The catch is that ordinary CRT is fragile: a small error in one remainder can cause a huge error in the result.
Why it matters
More robust ways to rebuild signals from partial information could improve radar target detection, moving-target tracking in synthetic aperture radar imaging, and the recovery of signals from low-cost modulo analog-to-digital converters. Because the method splits big jobs into small parallel ones, it could also ease the cost of handling large multidimensional data from imaging and sensing systems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Thomas Marzetta
University of Maryland, MD·Engineering
Develop true time delay (TTD) beamforming methods, which steer signals with time delays instead of phase shifts, for ultra-wideband antenna arrays covering the 7–24 GHz upper mid-band, using the Radon transform as the mathematical framework.
Hessam Mahdavifar
Northeastern University, MA·Engineering·Early-career
Generalize Plotkin Transform codes, the family containing Reed–Muller and polar codes, through nonlinear parameterizations, and search for new codes using machine learning, deep learning and gradient-descent optimization.
Ananth Shankar
Northwestern University, IL·Mathematics & Statistics·Early-career
Construct and study integral models of exceptional Shimura varieties, that is, descriptions by polynomial equations with whole-number coefficients for the varieties attached to exceptional symmetry groups.
The school
University of Delaware: 22 labs on PI Pages, $466M a year on research, 298 research doctorates a year.
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