Project Grant 2515247

This federal Project Grant award of $100,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research by Purdue University to develop advanced statistical methods for improving signal recovery and noise reduction in multiscale data domains. The key products and services to be delivered include:

• Innovative shrinkage and thresholding techniques applied in multiscale domains like wavelets to simplify complex data by selectively attenuating noise while preserving essential features, leading to more accurate and interpretable results.
• Exploration of quantum-inspired shrinkage methodologies that complement classical Bayesian and frequentist statistical frameworks.
• Development of adaptive block-shrinkage procedures with priors capturing dependence among wavelet coefficients, and novel thresholding strategies informed by extreme-value approximations and Bayesian decision rules.
• Integration of research findings into graduate and undergraduate courses, and creation of open-source software tools to promote reproducible research and broad access to the advanced statistical techniques.

This research aims to advance the theory and application of shrinkage estimation in multiscale settings, with a focus on quantum-inspired approaches, to address challenges in extracting meaningful information from large, noisy datasets across domains such as medical imaging, environmental monitoring, and telecommunications.