Modern science and engineering increasingly rely on extracting meaningful information from large and noisy datasets, such as those arising in medical imaging, environmental monitoring, telecommunications, and numerous other disciplines. This project develops advanced statistical methods that improve signal recovery and noise reduction through innovative shrinkage and thresholding techniques applied in multiscale domains like wavelets. In addition to classical computational tools, the project explores emerging directions involving quantum computing simulators to prototype quantum-inspired shrinkage methods, aligning with growing national and institutional emphasis on quantum technologies. These approaches simplify complex data by selectively attenuating noise while preserving essential features, leading to more accurate and interpretable results. The project integrates education by mentoring students at multiple levels, incorporating findings into graduate and undergraduate courses, and creating open-source software tools that promote reproducible research and broad access to cutting-edge statistical techniques. This research advances the theory and application of shrinkage estimation in multiscale settings, with a particular emphasis on quantum-inspired methodologies that complement classical Bayesian and frequentist frameworks. It develops adaptive block-shrinkage procedures employing priors that capture dependence among wavelet coefficients and introduces absolutely con