Grants and Contracts Details
Description
The rapid development of science and technology ushers in a new era of big data that requires
developing specialized algorithms to process a large amount of data. Signal processing and other related
techniques aim to recover signals of interest or some of their properties; this goal can be reduced to an
optimization question. Due to physical limitations of hardware, the size of the acquired data is in general
much smaller than that of the underlying signal, resulting in an ill]posed problem for signal recovery
with infinitely many solutions. Regularization techniques have been developed to address this inherent
ill]posedness. Despite being widely applied in low]dimensional signal processing, regularization has seen
limited use in processing high]dimensional data sets, especially those best represented by graphs, that
is, networks with sophisticated connections. This project aims to further develop graph]based
regularization techniques, with potential to revolutionize imaging and data analysis technologies in
many areas of data science.
This project aims to develop a useful graph]based regularization framework for various signal processing
problems, to address major theoretical and computational challenges for its applications, to provide
new interpretations of low]dimensional regularization techniques, and to demonstrate its capability for
handling large]scale data sets. The research has three objectives: (1) Develop novel graph]based
regularization techniques along with rigorous theoretical guarantees to handle the more challenging
signal processing problems and related inverse problems; (2) Develop efficient numerical algorithms to
solve the corresponding optimization problems; and (3) Conduct numerical experiments in imaging
applications to demonstrate the advantages of the proposed approaches in terms of accuracy and
efficiency. The research aims to improve data processing techniques and to infuse new insights into
mathematical signal and image processing, with a variety of applications such as medical imaging and
remote sensing.
Status | Finished |
---|---|
Effective start/end date | 7/1/19 → 6/30/24 |
Funding
- National Science Foundation: $186,006.00
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